Chapter 2.4, Problem 12AYU

In Problems 11-18, match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

To determine

To find: Match the given graph and the corresponding function.

Answer to Problem 12AYU

Solution:

Given graph is matched to the $\text{Absolute value function }f\left(x\right)=\left|x\right|\text{ that is }\left(G\right)$.

Explanation of Solution

Given:

It is asked to match the given graph and the corresponding function.

Given graph is :

It is matched to the graph $f\left(x\right)=\left|x\right|$. That is,

The domain of the absolute value function is the set of all real numbers; its range is the set of nonnegative real numbers. The intercept of the graph is $\left(0,0\right)$. If $x\ge 0$, then $f\left(x\right)=x$, and the graph of $f$ is part of the line $y=x$; if $x<0$, then$f\left(x\right)=-x$, and the graph of $f$ is part of the line $y=-x$. The absolute value function is an even function; it is decreasing on the interval $\left(-\infty ,0\right]$ and increasing on the interval $\left[0,\infty \right)$.

Therefore, the given graph is matched to the absolute value function $\left(x\right)=\left|x\right|$, that is $\left(G\right)$.