Chapter 1.7, Problem 26E

(A)

To determine

Identify the parent function

Answer to Problem 26E

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

Explanation of Solution

Given:

The function is $g\left(x\right)=4-{\left(x-2\right)}^2$

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 26E

The graph of $g$ is a reflection in the x-axis followed by right shift of two unit of the graph of $f\left(x\right)=x^2$ , then the resultant graph is shifted up four units.

Explanation of Solution

Given:

The function is $g\left(x\right)=4-{\left(x-2\right)}^2$

The graph of $g$ is a reflection in the x-axis followed by right shift of two unit of the graph of $f\left(x\right)=x^2$ , then the resultant graph is shifted up four units

(C)

To determine

Sketch the graph of $g$

Answer to Problem 26E

Graph is given below.

Explanation of Solution

Given:

The function is $g\left(x\right)=4-{\left(x-2\right)}^2$

The graph:

  

(D)

To determine

Find the equation of $g$ in terms of $f$

Answer to Problem 26E

The equation of $g$ in terms of $g\left(x\right)=4–f\left(x-2\right)$

Explanation of Solution

Given:

The function is $g\left(x\right)=4-{\left(x-2\right)}^2$

Write the g in term of f.

  $g\left(x\right)=4-{\left(x-2\right)}^2$ Given function

  $g\left(x\right)=4–f\left(x-2\right)$

Thus, $g\left(x\right)=4–f\left(x-2\right)$