Chapter 4.7, Problem 39PPS

To determine

To Find:

The equation of the graph from the given options.

Answer to Problem 39PPS

Option D is correct match.

Explanation of Solution

Given Information:

The graph is :

  

Concept Used:

ABSOLUTE VALUE FUNCTION :

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The absolute value of a number is its distance from 0 on the number line.

It is “V” shaped.

Parent Function : $f(x)=\left|x\right|=\{\begin{array}{l}x;x>0\\ -x;x\le 0\end{array}$

Domain : All real numbers

Range : All non-negative real numbers

Graph :

   $f(x)=\left|x\right|$

Calculation:

The given graph is “V” shaped , so it is Absolute Valued Function .

It has minimum value at (0,1) .

Since, the absolute valued function can also be defined as piecewise function.So, it matches the equation given in option D.

The equation is :

  $y=\{\begin{array}{l}2x+1:x>0\\ -2x+1:x\le 0\end{array}=\left|2x\right|+1$