Chapter 1.7, Problem 42E

(a)

To determine

To find: The expression for the parent function.

Answer to Problem 42E

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

Explanation of Solution

Given:

The given function is $g\left(x\right)=2\left[\left[x+5\right]\right]$ .

Calculation:

Consider the function $f\left(x\right)$ is,

  $f\left(x\right)=x$

Then shift the graph units to the left as,

  $f\left(x\right)=\left[x+5\right]$

Then multiply the graph by 2 as,

  $f\left(x\right)=2\left[x+5\right]$

(b)

To determine

To find: The sequence of transformation from $f$ to $g$ .

Answer to Problem 42E

The sequence of transformation is described.

Explanation of Solution

Given:

The given function is $g\left(x\right)=3-\left[\left[x\right]\right]$ .

Calculation:

Consider the function $g\left(x\right)$ is,

  $g\left(x\right)=x$

Then shift the graph 5 units to the left as,

  $g\left(x\right)=\left[x+5\right]$

Then multiply the graph by 2 as,

  $g\left(x\right)=2\left[x+5\right]$

(c)

To determine

To find: The graph for the function $g$ .

Explanation of Solution

Given:

The given function is $g\left(x\right)=2\left[x+5\right]$ .

Calculation:

The graph for the function is shown in Figure 1

  

Figure 1

(d)

To determine

To find: The expression for function $g$ in terms of function $f$ .

Answer to Problem 42E

The required notation is $2f\left(x+5\right)$ .

Explanation of Solution

Given:

The given function is $g\left(x\right)=2\left[x+5\right]$ .

Calculation:

The function $g\left(x\right)=2\left[x+5\right]$ in terms of $f\left(x\right)$ when $f\left(x\right)=\sqrt{x}$ is,

  $2\left[\left[x+5\right]\right]=2f\left(x+5\right)$

Then,

  $g\left(x\right)=2f\left(x+5\right)$