Unit
Inverse, Exponential and Logarithmic Functions
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Determining if a relationship is a function and if a relationship is 1 to 1. So I have a chart right here which has some data points and we’ll call this first column x and this second column y. What we are concerned with if it’s a function for every x there’s only one y or if it’s 1 to 1 for every x there’s y of for every y there’s just one x.
So looking at this, 1 goes to 5 2 goes to 6. So those are both 1 to 1 relationship for every x there’s only one y for every y there’s only one x. What we are concerned with here is 3 and 4 both going to 7. So the function part for every x there’s only one y.
If x is 3 y is 7, if x is 4 y is 7. So yeah for every x there’s only one y which means this is going to be a function. Second part is it one to one for every y is there only one x? And what we see here is if y is 7 there’s actually two x values so that tells us this is not actually 1 to 1.
Another example, here we have a different relationship again we are relating x and y for here this is just a straight or cross relationship. There’s x there’s a y and then there’s for every one x there’s one y and vice versa for every y there’s one x. So first part tells us that’s a function one x is one y. The second part for every y there’s also only one x tells us this is 1 to 1 as well. So the function is also one to one.
Our third example, our last example I want to see if this is a function. First part of the function is for every x is there only one y? Looking right here at number 1, if x is 1 we have y 5 x is 1 we also have y 6. So this tells us it’s not actually a function because for one x, number 1 there’s actually two different y’s. So this is not a function if it’s not a function it also cannot be 1 to 1 because part of being 1 to 1 is at first clause which means it also has to be a function. So if you have no for function it can’t be 1 to 1.
So just some examples of looking at some data making sure for every x there’s one y for a function and also for every y there’s one x just to make sure it's 1 to 1.