Good day everyone! For today's video, magre-review tayo para sa incoming quarterly test sa General Mathematics. At ang gagamitin nating reviewer are yung long test natin.
Kasi remember last time, hindi na natin na-checkan ito. So this will serve as our review for the first quarterly test. So we have 40 questions, sasagutan dito and I will be sharing with you techniques. On how to deal with multiple choice test item type ng exam. So, first question.
It is any relation that exists between two quantities, objects, persons, or group of persons, etc. So, sinasabi dito, it is any relation. So, obviously, we're talking about relation, letter C.
If you answered function, we're not really sure if the existence of relationship between the mentioned quantities, objects, persons, ay meron lang siyang unique domain. So, wala namang nabanggit na ganun. So, generally, ang sinasabi lang niya ay yung general relationship.
So, relation yun. We cannot also say it's an equation or set. Hindi pa naman natin yun pwedeng masabing ganoon.
So, it's a choice between function and relation. Which of the following relations describes a function? So, when we say function or third pairs ang binigay dito, madaling alamin kapag ka-function.
Now, titignan lang natin yung mga x nya, yung mga domain nya, kung ito ay unique. Example, letter A, 2, 1, we have 2, 1, 0, negative 1, negative 2. So, dito unique, walang naulit. So, obviously, letter A ang magiging sagot.
Natin yung may letter B, negative 2, 2, 2. So may dalawang naulit na domain. Sa letter C, merong naulit na 1 sa domain. Yun yung x coordinate, yung input.
So dito yung negative 3 naman. So only letter A. So madaling malaman yan kapag ordered pair.
Letter number 3. Which of the following illustrates a function? O kapag graph naman, we can use the vertical line test. No? Any part of the graph, kapag ginamit natin yung vertical line test, dapat, it will not intersect the graph on more than 2, 2 or more than 2 points.
So, ibig sabihin, dapat isang beses lang. Letter A. if we observe dito sa part na to, merong point na vertically aligned.
This is called a piecewise. Piecewise ito eh. But we're not necessarily saying it's a function.
So it's a piecewise function. equation. So, makikita natin na hindi sya function kasi may dalawang point tayo na nakita sa vertical line test. Letter B, wala naman akong nakikita so far on all parts.
So, the answer is letter B. Letter C kasi, we have 2. Letter D, we have maximum of 4. 4 yan. So, letter B tayo.
Number 4, the domain of f of x is, so this f of x or the given function in number 4 is called piecewise. Para malaman ang domain niyan, ang titignan lang natin ay itong conditions. for the domain.
So, nakikita natin kailangan lang natin emerge yan. So, x is greater than 1 and then x is less than or equal to 1. So, obviously, we're pertaining to kung itong ating number line. So, ito ang positive. Ito ang 0 natin, ito ang 1 natin. The first one is x greater than 1. So, pupunta siya dito.
And then, the second one is x is less than or equal to 1 kasama yung 1 then less than. So, actually, we are talking about all real numbers. So, the answer is letter C. Number 5, find f of x minus 2 if f of x is equal to 5x plus 3. So, this lesson is about evaluating functions.
Kaya lang, ang i-evaluate natin ay binomial. So, ibig sabihin, si x minus 2 ilalagyan natin sa x ni f of x. So, ito yung x natin dyan. So, yung x dyan papalitan natin ng x minus 2. So, we have f of x minus 5 is equal to 5 times x minus 2 plus 3. So, ito ay didistribute.
So we have 5x minus 10 plus 3 and then we have 5x minus 7. So that will be our evaluated function for f of x minus 2 and that is letter B. Number 6, what is the domain of f of x equals x squared over x minus 4? So, this one is a rational function.
So, para malaman ng domain yan, meron na tayong restricted value na kailangang malaman. So, actually, tingnan nyo yung... mga options.
Restricted ibig sabihin, not equal to. Kung mapapansin nyo yung option, meron na agad sagot eh, letter C. If there is an answer to this question.
Pero usually naman, if the questions are checked by by the teachers, meron talaga sya magiging sagot. So, dito, obviously, ang sagot ay letter C, not equal to 4. Kasi yun lang naman yung restricted value. Kasi ito, greater than, less than, and then less than. So, without any computation, yan ang magiging sagot. But, for general questions like this, ang kailangan lang naman ay yung the denominator, yan.
Equal 0. Yan lang naman ang formula for domain eh. Para malaman natin yung restricted value. So the answer is x equals 4 when you transpose the negative 4. So x should not be equal to 4 kasi magiging 0 siya. So letter C yung sa'yo. So that's how you could analyze that item.
Okay, let's go to 7 to 16. This is probably operations and probably combinations and evaluations of functions. For number 7, we are asked to add f and g. So we have the 3x plus 3x minus 2. That's the f and our g.
yun yung dalawa is x squared plus 2x minus 3 if we combine like terms 3x and 2x 3x and 2x is 5x negative 2 and negative 3 is negative 5 so ito yung ating addition of function f and g it's letter a Number 8, f plus g of 2. So, since nakukunin natin yung f plus g dun sa number 7, pwede na natin ilagay yung 2 as the value of x. Pero if not, kailangan muna natin kunin tong addition. of f and g. I-add muna natin sila tapos saka natin ilalagay yung 2. I-evaluate for x equals 2. Pero dito sa kasi meron na tayong clue from the previous question number 7. So ilalagay na lang natin sya. f of 2 is is equal to 2 squared plus 5 times 2 minus 5 that's equal to 4 plus 10 minus 5. This is positive 9. So the answer will be letter C.
And for number 9, maraming nagkakamali dito pagka subtraction of function na. So, h minus t. So, our h is x squared minus 5. And then, our t is 5x plus 4. Ang dami nagkakamali ito usually kapag subtraction ng function.
Kasi, paulit-ulit natin sinasabi na yung subtraction dito dapat i-distribute itong negative na ito. So, i-write natin yung minuend. So we have x squared minus 5 Tapos ito, pag dinistribute natin yan This positive 5x will become negative 5x This positive 4 will become negative 4 So dapat ganyan sya So combine like terms, ito lang naman ang i-cocombine natin So we will have x squared minus 5x Tapos yung minus 4 and minus 5 That's minus 9 So So we have answer letter B for number 9. Ang dami nagkakamali dyan sa subtraction, yung pagdi-distribute ng subtraction symbol, yung negative symbol. Question number 2. For number 10, h minus t of 5. So kanina, nakukuna natin itong h minus t, that's x squared. Anong nakakalit siya?
x squared minus 5x minus 9. x squared minus 5x minus 9. So ilalagay lang natin si 5. Dyan. So, 5 squared minus 5 times 5 minus 9. So, ito ay equal to 25 minus 25 minus 9. So, cancel ito, no? Kasi maging zero siya. So, the answer will be negative 9. yun lang sya kadali number 11 f of f times g of x since walang operation nakikita times yan kung may tuldok yan times din ang ibig sabihin yan so multiplication symbol in algebra. So, multiply lang natin si f and z.
So, let's have 3x minus 2 and then x squared plus 2x minus 3. So, i-distribute natin si 3x sa tatlong to. So, we'll have 3x cubed plus 6x minus 9x. Si negative to naman, i-distribute natin sa tatlong to. Negative 2x negative 4x negative 2x squared minus 4x plus 6. Combined like terms, wala naman like terms si 3x squared.
Si negative 2x squared, wala rin. And then for the x's, we have positive 6, negative 9. That's negative 3. And then negative 4, that's negative 7x. And then plus 6. So the answer for this is... Letter 3x squared minus 2x. 3x cubed, sorry.
3x cubed to. So nasa ng mga options natin. Ah, okay.
Wait lang. Magkamali tayo sa part na to. So, pag didistribute. Let's do it one more time.
So, si sir nagmamadali. Kasi kinakabala ako. Ayan. So, ito munang 3x times x squared. That's 3x cubed.
3x x times 2x, that's 6x squared, positive. 3x times negative 3, negative 9x. Yan, dun ako nagkamali.
Negative 2 times x squared, negative 2x squared. Negative 2 times 2x, negative 2x squared. x is negative 4x. And then, negative 2 times negative 3 is positive 6. So, combine like terms. 3x cubed.
Yung x squared natin ay 6x squared tsaka negative 2x squared. That's positive 4x squared. And then, negative 9x and negative 4x is negative 13x.
And then, plus 6. Kaya may sagot na tayo ng letter. Medyo naging at ano lang ako, no, pag nagmamadali talaga hindi nagiging OC sa pagdi-distribute, no, doon. So, huwag yung gagayahin yan.
So, dapat kailangan lagi kang maingat sa pagdi-distribute ng mga terms kapag multiplication. Doon na nga lang tatama, no, nagkamali pa. Ayan.
So, number 12, after multiplying, parang kasi lagi silang ganun yung pattern, no, ang ating value of x to be evaluated is negative 1. So, o, t, then negative 1 raised to 3 plus 4 negative 1 raised to 2 minus 13 times negative 1 plus 6. Eto, this is actually negative 1 sya dahil raised to odd. Negative 1 times 3, that's negative 3. And then, eto naman, dahil raised to even, that's positive 1 times 4, that's 4. Eto ay positive 13, and this one is positive 6. So, this one is positive 1, 14, 20. Letter D. Ayan. Number 13. T divide H, ito siya, T divide H.
So tingnan muna natin yung ano natin, no? Pag in-express natin siya in division, the T, that's 5X plus 4, divide our H, X squared minus 4. X squared minus 4, X squared minus 5. So kung mapapansin naman natin wala naman syang factor We can have this one as is So it should be letter B So meron kasi mga ganyan na kapag dinidivide na yung dalawang Ang polynomial, eh wala naman silang same factor. So we can have this one.
Number 14. What is the domain of T over H? Okay. Domain, again, titingin lang tayo sa ilalim.
Sa denominator. And equate it to 0. Tapos isasolve lang natin siya. X squared is equal to positive 5. And then, X is equal to positive and negative square root of 5. So ibig sabihin, Our domain should not be equal to positive and negative square root of 5. So, we can have, yun nakita natin sya, datum. So, set of real numbers except, very good, except, that means not equal to, except. So, our answer is letter B.
Number 15. T composed of H. So, si T composed daw siya ng H. It means that our H will be um The value of x for h.
For t, rather. So, t composed of h. So, h, i-evaluate natin sya.
We will put it in t. So, how do we say that? So, yung t natin is 5x plus 4. So, yung x dyan gagawin natin h. x squared minus 5 plus 4. So, we have to distribute this. 5x, ah sorry.
5x squared minus 25 plus 4. So, ito, like terms. So, we have 5x squared minus 21. So, letter C. Number 16. What is f composed of g?
So, si g ang ilalagay natin kay f. So, our f if 3x minus 2. So, our x there will be the g. The x squared plus 2x minus 3. minus 2. So, ito, didistribute natin sya dito sa tatlong to. And then, we will have 3x squared plus 6x minus 9. And then, copy minus 2. Ito, this will become negative 11. So, we will have a final answer of 3x squared plus 6x minus 11. And the answer is letter D.
Okay. Given the function at the right, this is a piecewise function, we're asked to evaluate f of negative 1. So kapag piecewise function, gagamitin natin yung mga domain niya sa gilid. Yun yung mga intervals of the domain. Kasi, katapat ng mga intervals of the domain are the corresponding functions na katapat nila. So, ang question dyan, ano gagamitin natin sa tatlo when we evaluate f of negative 1?
So, ang clue is you have to look at... the domain. Kung nasaan si negative 1. This one is less than negative 1. Probably not equal to negative 1. Kasi less than lang. Dito naman is from negative 1 up to positive 2. So x is greater than or equal to negative 1. So obviously dito tayo gagamit. Ito kasi ay greater than 2. So we will use this second function.
So we evaluate negative 1. F of negative 1 is equal to 3 times negative 1 minus 1. is equal to negative negative 3 minus 1 negative 5 so we have letter B number 80 A temperature surrounding of a cricket greatly affect the rate of the cricket chirps. The table below gives the rate that the cricket chirps at the given temperature. So, represent number 18 represent the number of chirps. per minute, g of t, a cricket makes at temperature t degrees Fahrenheit. So, eto daw ang ating function.
So, we have to represent this number of, number of chirps given the temperature. So, kung papansin muna natin yung Kung meron tayong pattern na makikita dito sa ating interval Kasi kung meron Kung ito ay arithmetic O meron tayong nakikitang pattern dyan Yun yung magiging one of the clue natin Dun sa mga functions natin Kasi usually kapag gumagawa tayo ng function Tapos may pamimilian naman We can look at the patterns muna Para meron tayong maging sagot Or matrim down natin yung mga option Kung mapapansin nyo Zero 86, 172, 258. Parang itong ano eh. May interval sya na 80. 86, this is 86, sorry. This is 86 times 1, this is 86 times 2, this is 86 times 3, this is 86 times 4, this is 86 times 0. So meron siyang multiplier na 86. Now, tignan natin sa mga options kung merong multiplier na 86. Letter D, walang multiplier.
Letter C, walang nagmumultiply ng 86. Ayun, meron dito isang nagmultiply. Tsaka, etong letter A. So, we have now options A and B alone. Now, kung meron tayong 86 ng multiplier, saan natin kukunin itong mga zero na to?
Ayan. So, titignan natin ngayon yung pattern dito sa temperature. So, So, Paano ito mag-zero?
Paano magiging zero ito? 1, 2, 3, at 4. Kasi may multiplier tayo na 86. Ano ang interval nila? Ang interval ay 20. 20 20 May interval na 20 So ibig sabihin Meron tayong magiging division na 20 dito You know A and B So kailangan natin i-divide sa 20 Yung given na 40 Pero kailangan dun sa first part natin Dapat maging 0 sya Paano magiging 0 to?
E di minus 40 So dapat meron tayong minus 40 dyan Yes, eto Ito kasi nag-multiply na siya agad. I-check natin. Kung nahihirapan kayo sa gantong way, pwede nyo i-check yung mga given.
Example, i-check natin itong letter B. Example, letter B yung napili nyo. Ilagay nyo si T na 40 dyan.
So, 86 times 40 minus 40 over 20. Kailangan na maging sagot dyan ay 0. So, dito pa lang. 86 times 40, ang laki na yan eh. Diba?
Tapos, hindi siya mag-zero. Automatically, hindi na. Ang laki nito masyado.
Minus 40 lang, divide 20. Try natin yung letter A. 86. Times T, that's 40 minus 40 over 20. This is actually 0. 0 over 20. This is actually 0 times 86, 0. So kapag may nakita kayong ganun na pwede nyo siyang i- Evaluate na lang isa-isa. I-try nyo kung alin dyan yung magpe-perfect fit na magiging equation natin.
Yun na yung probably magiging sagot natin. Chicheck nyo lang sila one by one. Checking which of the options are correct for the given. question. Pwedeng ganun.
Find the rate of a cricket if the temperature is 130 degrees. So, dahil letter A ang sagot natin, i-evaluate natin sya for G of 130 degrees. So, 86 times 130 minus 40 over 20. So, that is, 130 to ha.
So, this is 86 times 130, that's 90 over 20. That is equal to 86 times 60. 4.5 At ang 4.5 nito ay Aha Calculator So we have 344 plus 43, 387. The answer is letter B. So i-calculator na yung pagkaganyan. Multiply nyo na lang manually. If the temperature is below 40°F, would you compute for the rate of a cricket?
Again, if the temperature is below 40°F, would you compute for the rate of a cricket? Okay. Kasi dito, yung 40°F...
degrees pa lang, ay zero na. Ang tinatanong sa question, if the temperature is below pa nito. So, let's see kung kaya natin siyang makompute.
Of course, um, let's see the options. Yes, for as long as the data is given. Actually, kasi kapag nagbumaba pa ito sa 40, magne-negative na ito eh. No?
Example, let's say 30 lang. Try natin i-compute yan, given yung function natin. So, we have 86 times 30 minus 40 over 2. So that is equal to 86 times 10. Negative 10 over 20. That's negative 0.5 eh. 86 times negative 0.5.
And that is actually 43. So negative 43 yung magiging sagot dito. E wala naman tayong negative 43 na chirps. Di naman natin sila maririnig na tumutunog. Or yung mga crickets, tumutunog sila ng negative 43. Kasi the idea there is, sa real life situation, wala namang negative 43 talaga ng chips. So, ang sagot natin dyan probably is no.
Pamimilian na natin kung alin dyan sa dalawa. No, because the domain GFT starts from 40 and there's no temperature lower than 40 degree Fahrenheit. Letter D, GFT is not defined for temperature below 40 degrees because there is no negative number of chips.
Ayun, nabanggit na yung negative number of chips. So, the answer will be letter D. 21. The cost of hiring a catering service to serve food for a party is 150 per head.
150 per head, so may magmumultiply dito. For 20 persons or less. And then, 130 per head.
pesos per head for 21 to 50 persons, 110 per head for 51 to 100 persons, and 100 or more, the cost is at 100 pesos per head. Write a function that models the situation. Which of the following functions best describe the model?
Kasi ano siya, piecewise yung mga number of persons? 20 persons or less? Then 21 persons to 21 to 50 persons. So, ang kailangan natin ito unang i-check ay yung mga domain kung sasakto siya sa 100 or more.
Kung sasakto siya dun sa situation na given natin. 20 persons or less is less than or equal to 20. Less than or equal to 20. Less than or equal to 20. Yun, tama naman silang 4. Next, 21 to 50. So, this is greater than 20 But less than or equal to 50 So, tama to Tama to, tama to Okay, eto, mali na sya So, hindi na natin magiging option si letter B Okay, so para patuloy paresa man na sila ng sumunod na mga ano, na domain. So, probably yung tatlong yan.
So, ang pag-uusapan natin ngayon ay yung computational nila. Yung dito na. Actually, napakadali naman ang competition eh.
Kapag less than or equal to 20 yung tao, 150 per head. So, times x lang sya. Dapat, times x lang sya.
Ito rin, 130 per head. 130 times ilan yung tao. Ito naman, 110 times ilan yung tao.
So, So, dapat multiply lang. Dapat ito lang ang magiging option natin. Ito kasi, we don't know how they got this one.
May plus 20x pa. No? Yan.
So, our answer will be letter C. Yan lang yung next. Ganun lang naman ang computation usually kapag sa mga catering services. Multiply mo lang naman yung yung per head yun, who is the number of persons. So, letter C tayo.
So, yun. Meron siyang namuhunan siya ng 500,000 pesos para makapaggawa ng mga tables. chairs.
So, may dalawa syang klase ng tables and chairs. Yung isa, gawa sa NARA, binibenta niya ng 40,000 percent. Kasi isa naman, oak chair, binibenta niya ng 25,000 percent.
So, which mathematical model is it? The profit. So, profit.
So, profit is equal to, ano naman sya, diba? Profit is equal to, in this problem, meron syang puhuna na 500,000 eh. So, ima-minus natin lahat ng expenses dun sa kanya. capital na 500,000 so dapat ang makikita natin dito is f of x is equal to 500,000 minus yung cost nito yung cost nung um yun, kung cost nung Nara at saka nung Oak Chair so magkano ang magiging profit nya Uligtad pala, no? Kasi ang kanyang mga nabenta ay 40,000 na Nara chair tapos 25,000 para sa oak chairs.
So yun yung actually yung mga kinikita niya. Yung maminus natin doon ay yung magkano yung total niyang nagasto. So dapat, yung 40,000 na 4 Nara chairs, ilan yung nabenta niya doon?
ilang mga sets yung nabenta niya tapos yung 25,000 niya for the oak chair set yun, i-minus natin dyan yung nag-asas niya na 500,000 so ito ay profit is equal to what do you call this one this is the income minus minus the cost. Yun yung cost niya. So, the answer will be letter D.
Ayan. 23. Which of the following is not a rational function? So, pag sinabi natin rational, dapat meron syang variable x in either denominator or numerator or vice versa.
Pwede naman parehas. So, makapansin natin lang. Ang kakaiba lang dyan is letter B. Kasi pag sinabi natin rational function, dapat sya ay parehas na polynomial function. Yung numerator, denominator.
Ito naman identity, tapos isang monomial lang. Pwede naman yan. Pero yung letter B kasi natin, meron syang tinatag na radical function.
So this is not an example of a rational function. So that's an example of a radical function. Given the rational function 3x-1 over 2x plus 5, answer the following question.
The x-intercept is... So sa x-intercept, ang ating y ang 0. So may clue na agad kayo. Ang pamimilian nyo lang ay May sagot na kayo Ang pamimilian lang pala ay letter A Zero yung y natin dyan Tatandaan nyo, pag x intercept, y is zero Pag y intercept, the x is zero Ay, sorry The x is 0 naman. So, dito natitrim down yung lahala. Nandito na lahat yung mga sagat.
So, ganun yung patitrim down. So, paano naman natin makukuha yung x-intercept? Numerator lang ang gagamitin natin dyan.
Numerator equals 0. So, 3x minus 1 equals 0. 3x equals positive 1. Then, x equals 1 third. So, we have 1 third 0. Kaya, letter a ang sagat. Na, sa y-intercept naman, x equals 0 naman ang clue dito x equals 0 gagawin lang natin 0 yung x natin 3 times 0 minus 1 over 2 times 0 plus 5 probably 0 to so the answer is negative 1 fifth kaya letter d ang sagat so ganda lang kadali yung pag intercept vertical asymptote yung naging sagot natin sa domain sa denominator naman to so pag sinabi natin vertical asymptote asymptote, x equals 2. Yan ang clue natin dyan. So, probably lahat naman, okay, hindi na na magiging option ng a at saka d.
Hindi na na magiging option yan. So, mamimini tayo sa b at c. So, mas tumataas yung chance na tumama tayo. For the vertical asymptote, kailangan lang natin yung denominator. Denominator equals 0. So, yan yung clue dyan.
So, we have 2x plus 5 equals 0. So, 2x equals negative 5. x equals negative 5. over 2. So that's why the answer is letter P. The denominator equals 0. Equation for the horizontal asymptote so sa horizontal asymptote natin titignan lang naman natin yung degree pares naman yan raised to 1 so yung numerical coefficient lang ang magiging sagot yan so for horizontal asymptote kung ang ating vertical ay x equals 2 eto naman ay y equals 2 so wala na yung b at c and then this one is 3 halves so the answer will be letter a yun yung numerical coefficient Number 28. Which of the following is horizontal asymptote at y equals 0? So, probably, dapat pag merong value yung ating horizontal asymptote, hindi dapat equal yung degree. So, probably, eto kasi parehas 1. So, hindi yan sagot.
Eto din parehas 1. Ayan. So, our options is between letter B. B or letter D. Okay. So, laging yung tatandaan na ang horizontal asymptote ay magiging y equals 0 kapag mas mataas yung degree sa denominator.
So, eto sa letter B, x raised to 0 yan, 0 and then 1. x raised to 0 kaya 1 na lang sya. So, letter B ang magiging sagot. Dito kasi yung numerator ay 2, denominator ay 1. Eto ay y. Eto ay no horizontal asymptote. Now, horizontal asymptote yan.
So, probably letter B ang sagot natin. 29. Which function na sa vertical asymptotes x equals negative 3 and x equals 1 half? Vertical asymptote as x equals negative 3 and x equals 1 half. So, gagawin lang natin dito, dalawa yung pwede nyo. gawin.
Pwedeng gamitin natin itong tanong or pwedeng hanapin natin sa option yung may negative 3 or wala. So kapag dito tayo sa tanong magbe-base, yung babalita rin lang natin sya, x equals negative 3. Ito ay galing sa denominator, no? From the previous question. Ibig sabihin, ito ay x plus 3. Tapos yung x equals 1 half naman, yan ay galing sa 2x equals 1. Yan ay galing sa 2x minus 1. So ito yung dalawang factor ng denominator.
So kapag pinag-multiply natin yung dalawang yan, so x times 2x, that's 2x squared, and then negative x, and then 6x, and then negative 3. This is 2x squared plus 5x minus 3. So I think... So alin yung meron dyan denominator na 2x squared plus 5x minus 3. Letter B. Pwede naman na ang gawin natin dito ay isa-isahin natin yung mga option. Kasi dalawa tong binigay na value ng x.
So probably raised to 2. Dalawa kasi yan. Hindi yung ibig sabihin na mga zeros. Diba? So letter A and B lang din na talaga magiging options.
So denominator. Number 30. What is the equation for the horizontal asymptote of the graph of the function At the right Parisontal asimto Ito sya, itong na broken line na to horizontal asymptote, etong broken line na ito na horizontal tumama sya sa positive 4 so yan ay y-axis equals 4 so we have lettered what are the x-intercepts of the graph so eto, numerator ulit yan, parang exercise lang din yung nangyari sa long test natin may mga paulit-ulit na tanong so kailangan natin itong i-factor x plus x plus 7 and then x minus 3 kasi pag pinag multiply yan negative 21 pag pinag add positive 4 so x equals negative 7 and x equals positive 3 letter B Which of the following function has a hole at x equals 5? So at x equals 5, pag sinabi yung hole natin, yung sabi, eto yung factor na kinancel natin na makikita natin both on numerator and denominator. So x equals 5 means that that factor is x minus 5 equals 0 yan, diba?
Yan yung, ano, nireverse natin yung process. So, merong x minus 5 na na-cancel. So, wala kang makikita yung x minus 5 dyan, wala rin dito.
Dito, sa dalawang to, actually, pares lang silang item. item. This is actually, yung parehas na yan is x minus 5, x plus 5 yung numerator, tsaka x minus 5. So, nag-cancel tayo ng x minus 5 dyan. So, yun yung sinasawag natin na whole. So, the answer is either A or C.
For item number 33, what is the zeros of x-3 over x plus 2 equals 0? So pag sinabi natin zeros, ang technique lang dito kapag rational function, yung numerator, equate niyo lang siya sa zero. So yan lang ang technique dyan.
Kunin ang numerator, tapos i-equate sa zero. And then, isolve natin yung x dyan. So, x equals 3. Yun yung zeros na tinatawag natin, or zero or zeros of a rational equation.
So, ang answer ay letter A. What is the first step to solve for this rational equation? Equation. Letter A, simplify the equation. Letter B, find the LCM.
Letter C, guess the value of X, then solve. Syempre hindi yung guessing. Find the zero of the equation.
Of course, not this one. So ang gagawin lang natin dito, lagi naman natin yung unang ginagawa is we find the LCM and we multiply that to the whole equation. So the correct answer is letter B.
Tingnan yung y axis. Negative 1, positive 1. This is decimal, less than negative 1. Ito ay decimal din na greater than, less than positive 1 na nun siya. So dahil magkakaiba yan, the best way to describe the graph of this one is to identify its y-intercept.
That is when x is equal to 0. So may ordered pair na tayo. So y is equal to 1 over 0 minus 4. That is y equals 1 over negative 4. So ang ating ordered pair is 0, negative. 1 fourth. So the answer will be this one. So the answer is letter C.
So pagkakasimil mga features na tayo, may mga graph tayo sa pagpipilian, ang pinakamagandang gawin dyan, hanapin natin yung pagkakaiba ng mga graph, tapos yun yung hanapin natin dun sa given equation. Mas mapapadali yung pagsasagot natin. 36. How many points and intervals are needed to be test for the...
inequality to. For the inequality, so, alam naman natin na to identify the points, we are going to find the value of x when the numerator and the denominator is set to 0. So, points muna tayo. Tingnan nyo, magkakaiba yung points dyan.
So, without looking further on the interval, sa points pa lang malalaman na natin ang sagot. So, the numerator is x minus 3 equals 0. So, x equals 3. So, we have 1 point. For the denominator, x plus 2 equals 0, x equals negative 2. So, we have the second point. So, actually, we have 2 points.
And then, if we have 2 points, 2 points, let's just add 1, that will be equal to the interval. Kasi, syempre, kung sa number line, meron kang dalawang points, ilang interval yung kailangan mong itest? We have 1 interval, 2, and then 3. So the third interval. So we have three intervals.
So the correct answer is letter B. Okay, again, to find the number of points, kailangan natin isolve yung value of x when the numerator and the denominator are set to zero. So ito yung sa numerator, ito yung sa denominator, ilan yung value na nasolve natin?
Overall, we have two. So ilang interval? Three. Ganyan. 37. The following are inverse functions except Okay, so paano nating malalaman kung mga mag-i-inverse function sila?
Or they are inverse of one another? So kailangan nating isolve yung composition of function like f of f raised to negative 1 of x. So kapag ano natin yan, na-solve natin yan, either of the two, or mag-composition lang tayo dyan, kapag x ang sagot, that means they are inverse.
So unahin natin yung letter A. So ilagay natin to dito. So we have 2x over 2, so we have x. So the first one is an inverse. Number 2, let's have 7x minus 2 minus 2 over 7. This is 7x minus 4 over 7, so cannot be simplified.
So letter B is not an inverse function. Letter C, pag nilagay yan dito, automatic x naman yan. Ganon din dito, parang letter A lang din. Madali natin siyang makikita kapag nag-composition tayo.
Composition of function 38 Which of the following is not the graph of inverse function? Ayan Madaling maraman yung graph of inverse function, diba? Aalamin lang natin kung merong reflection na nangyayari pari dun sa graph, about the y equals x. So, ayan yung ating mirror. So, imagine natin yun yung mirror natin.
Tingnan natin kung eto ay nag-reflect dito. Kasi, di ba bilanggit ko na sa inyo, when you say reflect, iba sya dun sa duplicate. Kasi pag duplicate, kapag humarap ka sa mirror, yung kanan mo pag tinignan mo yung mirror, nandun sya sa kaliwa so yun yung nagre-reflect kapag duplicate kasi they are equivalent images or congruent images, kung ano yung nasa right yun din yung nasa right ng kabilang images katulad nito o yan bumaligtad sya, so it means it's also inverse function eto naman, this is very confusing kasi hindi mo malalaman kung nag-inverse sya, kasi symmetrical yung image...
So, yan. So, inverse din yan. Ito, it's actually duplicated. Dapat yung isang graph niya ay pagganito.
Kung talagang siya ay naka-mirror. Kasi, anong nangyari? Nag-letter S din yung graph niya. So, this one is not an inverse function.
g of f letter S. si G. F is composed of G. On the other hand, G is composed of F. Dapat pag sinunod either, it should be X.
Number 40. Ito marami ng kamari dito. Negative 2, 3. Positive 2, 3. 2 negative 3 is a point on F of X, yun yung isa sa mga point niya. And then G of X contains 8, 0. If F of X and G of X are inverse functions, determine other points they contain aside from the aforementioned. So kung inverse functions sila, dapat eto, makikita mo siya dito as inverse na 0, 8. At eto, makikita mo siya sa kagalimutan. nila na negative 3, 2. So, yan yung hakanapin natin dito.
So, si negative 3, 2, dapat nasa g of x sya. So, mali ito. Negative 3, 2, dapat nasa g of x sya.
And 0, 8 nasa f of x. So, So, the correct answer is letter B. So, yan. So, ito yung offer ko na reviewer para sa ating quarterly test. Kaya, I hope you watch this video.
At, anuhin nyo, aralin nyo mabuti. Of course, this will be similar to the quarterly test. Kasi, yun din naman ang coverage.
So, good luck. Kalingan nyo sa exam. Sana mataas ang makuha yung score. On the end, your score on the assessments are the return of investments ng lahat ng inyong...
pinaghirapan for the whole quarter. Ano man na maging score nyo dyan, pandaan nyo, mahal ko pa rin kayo. Kaya lang, pag mababa yung binigay ko sa inyong grade, mahal ko pa rin kayo kaya walang samaan ng loob.
See you again next time for the second quarter. Bye-bye!