How do I determine if a function is one-to-one?
For example, is log4(x+2) a one-to-one function?
And is x^2+3 a one-to-one function?
Should I graph it to figure this out, or is there another way?

Question

How do I determine if a function is one-to-one?
For example, is log4(x+2) a one-to-one function?
And is x^2+3 a one-to-one function?
Should I graph it to figure this out, or is there another way?

solomonzelman · Answer

For a function to be a one-to-one, it must pass the
(1) Vertical Line Test,
(2) Horizontal Line Test.

In other words, if you know that you can draw a vertical or a horizontal line somewhere such that this line will cross two points on a function, then you say that the function is NOT one-to-one.

solomonzelman · Answer

|dw:1456418520374:dw|