Chapter 1.7, Problem 49E

i.

To determine

To calculate: Use the graph of $f\left(x\right)=\left|x\right|$ to write an equation for the function represented by graph. $f\left(x\right)$

  

Answer to Problem 49E

The function of given graph is written by $y=-\frac{1}{2}\left|x\right|$

Explanation of Solution

From the above graph we can see that above graph is reflection of $f\left(x\right)=\left|x\right|$ , reflected in x-axis and vertically compressed by a factor say, t

So, function of above graph can be written as $y=t\left|x\right|\cdots \left(i\right)$

Now, we can use above given point $\left(4,-2\right)$ to find value of t

Put $\left(4,-2\right)$ in equation $\left(i\right)$ ,

  $\begin{array}{l}-2=t\left|4\right|\\ -2=4t\\ t=-\frac{1}{2}\end{array}$

Now by put the value of y in equation $\left(i\right)$

  $y=-\frac{1}{2}\left|x\right|$

ii.

To determine

To calculate: Use the graph of $f\left(x\right)=\left|x\right|$ to write an equation for the function represented by graph.

  

Answer to Problem 49E

The function of given graph is represented by $y=3\left|x\right|-3$

Explanation of Solution

From the above graph we can see that above graph is reflection of $y=3\left|x\right|-3$ , shifted down by 3 units and vertically stretched by a factor say, t

So, function of above graph can be written as $y=t\left|x\right|-3\cdots \left(i\right)$

Now, we can use above given point $\left(-2,3\right)$ to find value of t

Put $\left(-2,3\right)$ in equation $\left(i\right)$ ,

  $\begin{array}{l}3=t\left|-2\right|-3\\ 6=2t\\ t=3\end{array}$

Now by put the value of y in equation $\left(i\right)$

  $y=3\left|x\right|-3$