Chapter 4.6, Problem 53S

To determine

To identify: The type of function represented by graph.

Answer to Problem 53S

The absolute value function is represented by the graph.

Explanation of Solution

Given information:

  

Formula used:

Transformation of functions:

Translates graph h units left. $f(x+h)$

Translates graph h units right. $f(x-h)$

Translates graph k units up. $f(x)+k$

Translates graph k units down. $f(x)-k$

Calculation:

The parent function of absolute value functions is $f(x)=\left|x\right|$ . The domain of $f(x)=\left|x\right|$ is the set of real numbers , the range is the set of real numbers greater than or equal to 0.

The parent graph is shifted towards left by $f(x+h)$ and then the graph is shifted downwards by $f(x)-k$ .