I'm ranking the top 10 most common functions in a fun and hopefully informative tier list our first function is the linear function y = x some people might call this function boring but I like how predictable it is y is equal to X how much easier could the calculations be all linear functions have a constant rate of change which means the slope is the same between any pair of points it's really easy to graph just use your slope which is rise over run to plot your points and that's probably the one thing that mostly everyone remembers from high school math there are lots of easy and useful applications such as calculating income from hourly wages doing temperature conversions or using the distance formula where distance is equal to speed time time this is definitely an a tier function next up we have the quadratic function y = x^2 the graph of this forms a cool shape called a parabola it's symmetrical which is nice and it has an absolute Max or Min called a Vertex there are lots of applications that involve quadratic relationships including projectile motion and revenue optimization and who doesn't like to optimize revenue or model how gravity affects a projectile's motion this function also goes in a tier next up we've got the square root function y equals the square root of x this function has a restricted domain and it only lives in one quadrant but the graph kind of looks like the square root symbol itself so that's kind of neat if you try and make x negative you get an imaginary number which sounds interesting but it's pretty complex square roots do show up in lots of formulas in trigonometry statistics and physics some places where you will find the square root function are the distance formula the quadratic formula standard deviation formula and the formula for the period of simple harmonic motion even though this function has lot of interesting applications why do we so often only consider the positive or principal square root what about the negative square root of a number for that reason let's put this function in C tier next up we have the absolute value function y equals the absolute value of x this function is never negative which sounds like a good thing but that has to be exhausting making everything that is negative turn into a positive sounds kind of fake to me f tier next up we have the sign function yal sin x this function does have a range that's restricted to being between Nega 1 and one but one cool thing is that there's an infinite number of solutions for X that have a y value that's between Nega 1 and one also connections to the unit circle help open up the world of trigonometry there's tons of applications with any periodic relationship like tital patterns vibrations temperature amount of sunlight sound wave waves and simple harmonic motion and voltage without trig functions there wouldn't be trig identities which are always fun to try and prove this function has to go s tier next up we have the rational function y = 1 /x any function with ASM tootes is interesting are we sure it just approaches those lines more and more closely it must get there eventually right haven't you heard of Achilles in the tortoise this function makes you actually think about the idea of a limit and infinity which are both very important ideas in math B tier next up the exponential function y equal 2 ^ x would you rather get $1,000 every day for a month or get one cent on day one two cents on day two four cents on day three 8 cents on day four and it keeps doubling until the end of the month think about that and you'll understand the power of exponential growth there are many interesting applications that involve exponential functions such as radioactive decay compound interest Half-Life and population growth the rate of increase in an exponential growth relationship can be amazing when looking at how many times you would have to fold a piece of paper for it to be thick enough to reach the moon or financial applications but the rate of increase of exponential growth can be pretty terrifying when looking at the spread of disease for that reason this function goes in B tier next up we have the log function yal log of x log functions can be used to analyze values that have a massive range of magnitudes by taking the logarithm of a data set it compresses its range and makes it easier to analyze this is done with the RoR scale sound intensities and also pH levels there's a couple special logarithms you have to know about the common logarithm and the natural logarithm and you should know that logarithm are the inverse of exponential functions since exponential functions were in B tier the inverse of B tier I guess that would have to be C tier so let's throw log X in C tier next up we have the cubic function y = x Cub when graphing this function I always find it hard to get the curve just right but it does have rotational symmetry which is kind of neat but finding cool applications of this function is a bit of a stretch Maybe bazer curves for computer animated drawings I don't know F tier next up we've got the constant function y equals 3 this is the most reliable function for every input you give it gives the exact same output it never changes its rate of change or its slope is zero it's the easiest function to differentiate it's very predictable the range is just a Singleton set the only downside of this function I can think of is that you need a ruler to graph it but still this function goes s tier let me know down in the comments any functions I missed and what tier you would put them in Jensen move