[Applause] hello to all my wizards this is senior pablo and welcome to our second channel the senior pablo tricks and trivia for our first video we're going to answer a first periodic test in grade 11. if you want to check the questions you can go to our community section in senior pablo tv and you can find the questions there okay let's start our question number one okay let's check question number one which of the following sets of ordered pairs define a function we define a function if there is no x-coordinate or the x-coordinate must not be repeated so let's check our choices for letter a the x-coordinates are negative 3 negative 2 negative one and negative two we notice that negative two is repeated twice so letter a is wrong how about letter b one two three and four so letter b is our answer because our x coordinate x coordinate is not repeating okay and you can take a look at that letter c and letter d in letter c 0 is repeated twice as our domain and for letter b letter d1 is repeated once so the correct answer in number one is b next number two which of the following graph shows for every value of x there is only one value of y so in here we're going to use the vertical line test you can check our playlist to understand the vertical line test so in this case our answer is letter b and now let's proceed in number three which of the following or which of the following arrow diagrams shows that y is a function of x so we're dealing with the correspondence we know that a function can be one-to-one or too many so in this case letter a is not our answer because our correspondence is many to one letter b we have many to one that's not a function for letter c we have one too many so that is a function so the answer in number three is letter c and letter d that is many to one which is not a function so number one is b number two is b number to the is c next number four which of the following graph does not define a function we're going to use does not define so we're going to use the vertical line test because this is a graph and notice that the only graph in number 4 that does not define a function is letter d the y because if we're going to use the vertical like this it will touches the graph twice okay next number five find the value of f of x so we're going to solve this f of x is equal to four x squared plus three x minus fifteen when x is negative two so let's solve f of x is equal to four x squared plus three x minus fifteen when x is equal to negative two so substitute the value of x so four times negative two squared plus three times negative two minus three four times negative two squared that is positive four positive three times negative two that is negative six then copy minus fifteen now we have four times four sixteen minus six minus fifteen sixteen minus six that is ten minus fifteen negative five so when x is negative 2 the function will give us negative 5 so that is letter d dot so let us write our answer here number one is b number two b number three c number four the number five is d and now let's proceed in number six find the range given the function f of x is equal to x over two plus three where x is an element of 0 2 4 6 and 8. so we have the function f of x is equal to x over two plus three then x an element of zero two four six and 8. we're going to find f of x so let's substitute if we have f of 0 that will give us 0 over two plus three zero divided by two that is zero plus three what is zero plus three that is two if we have f of two two we have two over two plus three two over two that is 1 or less than e that will give us next i have a 4 that is 4 over two plus three four divided by two that is two plus three oh sorry one plus three is four okay sorry for that two plus three is five and six notice a pattern two four a three four five of course we have six and seven so that is letter three four five six seven letter d letter d for number six next number seven given f of x is equal to x raised to four minus one and g of x is equal to x minus z which of the following value corresponds to f compose of g of three we're going to solve so we have f compose of g of three so this is the same as f of g g of three so f of what is our g of three so let's get g of x so we have g of x is x minus two so x minus two this is two so we have three minus two so now we have f of one hey just change the x to our volume which is three so three minus two that is one now let's find f of one in number seven f of x is equal to x raised to four minus one so we're going to find f of one so one raised to four minus one now one raised to four that is one minus one will give us zero so f compose of g of three is equal to zero so number seven is letter c okay that is number seven next number eight number eight given f of x is equal to three x over x minus 2 and g of x is equal to 2x minus 1 over x minus 2 what value of x will make the product of f of x and g of x undefined so to make our function undefined let us equate the denominator to zero for f of x our denominator is x minus two so we have x minus two is equal to zero therefore for g of x for f of x x is equal to two how about the g of x the denominator is x minus two equal to zero so x is equal to positive to make the functions undefined the value of x must be two so number eight is letter c so one to eight so this is our part one of our tricks and trivia checking of the periodic tests of general mathematics stay tuned for our part 2 this coming saturday thank you for watching senor pablo tricks and trivia you