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A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

$ f(t) $ is the height of a football $ t $ seconds after kickoff.

not a 1 -to-1 function.

01:35

Jeffrey P.

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

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to figure out if this is a 1 to 1 function. Let's just make a rough sketch of what's going on. So we have time and we have the height of the football on. What's going to happen is the football is probably going up first and then it's on its way back down. So is that a 1 to 1 function? Well, To be a 1 to 1 function, it must pass the vertical line test for every X value. There's only one Y value and the horizontal line test for every Y value. There's only one X value, so it passes the vertical line test. That's what makes it a function in the first place, but it fails a horizontal line test because there are places where it passes through multiple points on a horizontal line. So that was a fail. So, no, this is not a 1 to 1 function

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