Chapter 1, Problem 100RE

a.

To determine

To identify : the parent function.

Answer to Problem 100RE

The parent function is $f\left(x\right)=x^2$.

Explanation of Solution

Given information :

The function is $h\left(x\right)={\left(-x\right)}^2-8$.

form the function provided in the question it can be observed that the function is transformed by the parent function of $f\left(x\right)=x^2$.

b.

To determine

To describe : the sequence of transformations $f$ to $h$.

Answer to Problem 100RE

reflect the graph of parent function $f\left(x\right)=x^2$ in the y -axis and then shift eight unit downwards

Explanation of Solution

Given information :

The function is $h\left(x\right)={\left(-x\right)}^2-8$.

since parent function is $f\left(x\right)=x^2$ ,to transform the graph form $f$ to $h$ , first reflect the graph of parent function $f\left(x\right)=x^2$ in the y -axis and then shift eight unit downwards.

c.

To determine

To draw : the graph of function h.

Explanation of Solution

Given information :

The function is $h\left(x\right)={\left(-x\right)}^2-8$.

graph : first, to graph the parent function use the point plotting,

x	1	-2	-3	-4
y	1	4	9	16

Now ,reflect the graph of parent function $f\left(x\right)=x^2$ in the y -axis and then shift eight unit downwards.

Thus, the graph can be obtained as:

  

Interpretation: from the above graph it can be observed thatto graph $h\left(x\right)={\left(-x\right)}^2-8$ ,reflect the graph of parent function $f\left(x\right)=x^2$ in the y -axis and then shift eight unit downwards.

d.

To determine

To find : the function h in the terms of function of f.

Answer to Problem 100RE

the function h in the terms of function of f is $h\left(x\right)=f\left(-x\right)-8$.

Explanation of Solution

Given information :

The function is $h\left(x\right)={\left(-x\right)}^2-8$.

Calculation : since $f\left(x\right)=x^2$ , to write the function h in the terms of function of f substitute $f\left(x\right)=x^2$ in the function h.

  $\begin{array}{l}h\left(x\right)={\left(-x\right)}^2-8\\ h\left(x\right)=f\left(-x\right)-8\text{ [substitute }f\left(x\right)=x^2]\end{array}$

Hence, the function h in the terms of function of fis $h\left(x\right)=f\left(-x\right)-8$.