Functions

Functions

What is a function?

An equation will be a function if...

for any x in the domain of the equation (the domain is all the x’s that can be plugged into the equation) the equation will result exactly one value of y.

Example 1: Let's determine if each of the following are functions.

1. y= x²+1

1. y² = x+1

Solution

1. The first one is a function.

Given an x there is only one way to square it and then add 1 to the result and so no matter what value of x you put into the equation there is only one possible value of y.

1. The only difference between this equation and the first is that we moved the exponent off the x into the y. This small change is all that is required, in this case, to change the equation from a function to something that isn’t a function.

To see that this isn’t a function is fairly simple. Choose a value of x, say x=5 and plug this into the equation.

y ²= 5+1=6

Now, there are two possible values of y that we could use here. We could use y = 3 or y = −3.

Since there are two possible values of y that we get from a single x this equation isn’t a function.

Remember that this only needs to be the case for a single value of x to make an equation not be a function.

Because of what happens at x=5 this equation will not be a function.

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