Chapter 12, Problem 1TYWP

To determine

The correct option that completes the provided statement “In a one-to-one function”.

Answer to Problem 1TYWP

Solution:

The correct option is d that is “each x value corresponds to only one y-value and each y-value corresponds to only one x-value”.

Explanation of Solution

Given Information:

The provided options are:

a. each $x$-value corresponds to only one $y$-value.

b. each $x$-value corresponds to one or more $y$ values.

c. each $x$-value is the same as each $y$-value.

d. each $x$ value corresponds to only one $y$-value and each $y$-value corresponds to only one $x$-value.

In a one-to-one function, each $x$ value corresponds to only one $y$ value and each $y$-value corresponds to only one $x$-value.

For example:

Consider a function:

This function is not one-to-one because the y value $7$ corresponds to two x values $2$ and $3$.

Consider another function:

This function is one-to-one because each $x$ value corresponds to only one $y$-value and each $y$-value corresponds to only one $x$-value.

Thus, the correct option is d. each $x$ value corresponds to only one $y$-value and each $y$-value corresponds to only one $x$-value.