Chapter 4, Problem 4CA

To determine

To select: The functions that are shown in the given graph.

Answer to Problem 4CA

The functions that are shown in the given graph are $g(greenline),h(redline),k(purpleline),q(blueline).$

Explanation of Solution

Given information: A function $f(x)=x-1$ and a graph is given.

Given function is $f(x)=x-1$.$-(i)$

Let us write all the given function in slope-intercept form ( $y=mx+b$ , where $m$ is the slope and $b$ is the $y-\mathrm{int}ercept$ ).

  $g(x)=f(x+2)$$=(x+2)-1$ $=x+1$

  $\Rightarrow m=1,b=1$

Clearly, the green colored line is the graph of $g(x)=x+1$ .

  $h(x)=f(3x)=3x-1$

  $\Rightarrow m=3,b=-1$

Clearly, the red colored line is the graph of $h(x)=3x-1$ .

  $k(x)=f(x)+4=(x-1)+4=x+3$

  $\Rightarrow m=1,b=3$

Clearly, the purple colored line is the graph of $k(x)=x+3.$

  $p(x)=f(-x)=-x-1$

  $\Rightarrow m=-1,b=-1$

Clearly, there is no line with slope $-1$ and $y-\mathrm{int}ercept$

  $-1$ .$r(x)=3f(x)=3(x-1)=3x-3$

  $\Rightarrow m=3,b=-3$

Clearly, there is no line with slope $3$ and $y-\mathrm{int}ercept$ $-3$ .

  $q(x)=-f(x)=1-x=-x+1$

  $\Rightarrow m=-1,b=1$

Clearly, the blue colored line is the graph of $q(x)=-x+1$ .

Thus, the functions that are shown in the given graph are $g(greenline),h(redline),k(purpleline),q(blueline).$