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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.

We could draw a horizontal line that intersects the graph in more than one point. Thus, by the Horizontal Line Test, thefunction is not one-to-one.

01:22

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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we're deciding here whether or not this function is 1 to 1 and to be 1 to 1. Every X value must have only one y value, and every y value must have only one X value. So for every X value to have only one y value, it must pass the vertical line test. So if you pass a vertical line through anywhere, you'll only pass through one point, not more than one. So it does pass that test, but it also must pass the horizontal line test in order for every Y value to have only one X value. And so, if you pass a horizontal line through, you can only pass through one point, not more than one. So we can see that it fails the horizontal line test because there are some why values that have multiple X values. Therefore, it is not a 1 to 1 function

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