Chapter 1.7, Problem 22E

(A)

To determine

Identify the parent function

Answer to Problem 22E

The parent function $f$ is quadratic function so, $f\left(x\right)=x^2$

Explanation of Solution

Given:

The function is $g\left(x\right)=x^2–2$ .

The parent function $f$ is quadratic function so, $f\left(x\right)=x^2$

(B)

To determine

Find the sequence of transformation from f to g

Answer to Problem 22E

Sequence parent graph is $f\left(x\right)=x^2$ so, $g\left(x\right)$ is obtained by shifting the graph of $f\left(x\right)$ down two units.

Explanation of Solution

Given:

The function is $g\left(x\right)=x^2–2$

The parent graph is $f\left(x\right)=x^2$ so, $g\left(x\right)$ is obtained by shifting the graph of $f\left(x\right)$ down two units.

(C)

To determine

Sketch the graph of g

Answer to Problem 22E

Graph is given below.

Explanation of Solution

Given:

The function is $g\left(x\right)=x^2–2$

The graph:

  

(D)

To determine

Find the equation of g in terms of f

Answer to Problem 22E

The equation of g in terms of f $g\left(x\right)=f\left(x\right)–2$

Explanation of Solution

Given:

The function is $g\left(x\right)=x^2–2$

Write the $g$ in term of $f$ .

  $g\left(x\right)=x^2–2$ Given function

  $g\left(x\right)=f\left(x\right)–2$ Replace $x^2$ be $f\left(x\right)$

Thus, $g\left(x\right)=f\left(x\right)–2$