Chapter 1, Problem 79RE

a.

To determine

The parent function of f

Answer to Problem 79RE

Parent function will $\left[x\right]$

Explanation of Solution

Given:

The function is given as:

  $h\left(x\right)=5\left[x-9\right]$

Rule for shifting the function horizontally is;

  $h\left(x\right)=f\left(x+c\right)$ ( forward )

  $h\left(x\right)=f\left(x-c\right)$ ( backward )

Now, rule for shifting the function vertically is;

  $h\left(x\right)=f\left(x\right)+c$ ( upward)

  $h\left(x\right)=f\left(x\right)-c$ ( downward )

Here, function is given;

  $h\left(x\right)=5\left[x-9\right]$

Therefore parent function will be $\left[x\right]$

b.

To determine

Sequence of transformation from f to h.

Answer to Problem 79RE

It can be found by subtracting nine unit from parent function and then multi[plied by5.

Explanation of Solution

Given:

The function is given as:

  $h\left(x\right)=5\left[x-9\right]$

Rule for shifting the function horizontally is;

  $h\left(x\right)=f\left(x+c\right)$ ( forward )

Here, c is real constant.

Now, rule for shifting the function vertically is;

  $h\left(x\right)=f\left(x\right)+c$ ( upward )

Here, c is real constant.

Here, function is given;

  $h\left(x\right)=5\left[x-9\right]$

It can be found by subtracting nine unit from parent function and then multi[plied by5.

c.

To determine

To sketch :

The graph of h.

Explanation of Solution

Given:

The function is given as:

  $h\left(x\right)=5\left[x-9\right]$

Plot of h is ;

d.

To determine

Function notation to write h in terms of f

Answer to Problem 79RE

h in terms of f will be;

  $h\left(x\right)=5f\left(x-9\right)$

Explanation of Solution

Given:

The function is given as:

  $h\left(x\right)=5\left[x-9\right]$

h in terms of f can be written as;

  $h\left(x\right)=5f\left(x-9\right)$