Chapter 3.5, Problem 4CYU

To determine

The transformation in each function related to the graph for $g\left(x\right)=0.25x$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=x$ .

Transformed function is $g\left(x\right)=0.25x$ .

Calculation:

Standard equation of slope intercept form is expressed as follows:

  $y=mx+c$

Here, m is slope and c stands for constant.

Write the given function in the standard slope as function is linear intercept form as follows:

  $y=\left(1\right)x+0$

Here, constant is 0 and slope is 1.

Write the transformed function in the standard slope as function is linear intercept form as follows:

  $\begin{array}{l}y=0.25x+0\\ =\frac{1}{4}x+0\end{array}$

Here, constant is 0 and slope is 0.25.

Thus, the function $f\left(x\right)=x$ has 4 times slope as of function $g\left(x\right)=7x$ in graph which is shown below: