Chapter 9.1, Problem 37PPE

Solution

(a)

To graph: Thefunction $g\left(x\right)$ and compare it to the function $f\left(x\right)$ .

Given information:

The given function $f\left(x\right)=x^2+2\text{and}g\left(x\right)=3f\left(x\right)$ .

Calculation:

Consider the given function $f\left(x\right)=x^2+2\text{and}g\left(x\right)=3f\left(x\right)$ .

Find $g\left(x\right)$ .

  $\begin{array}{c}g\left(x\right)=3\left(x^2+2\right)\\ =3x^2+6\end{array}$

Now, draw the graph,

  

Interpretation:

The graph of $g\left(x\right)$ is lifter up by 6 unit and scale down by 3 unit compared to the graph of $f\left(x\right)$ .

(b)

To graph: The function $g\left(x\right)$ and compare it to the function $f\left(x\right)$ .

Given information:

The given function $f\left(x\right)=x^2+2\text{and}g\left(x\right)=f\left(3x\right)$ .

Explanation:

Consider the given function $f\left(x\right)=x^2+2\text{and}g\left(x\right)=f\left(3x\right)$ .

Find $g\left(x\right)$ .

  $\begin{array}{c}g\left(x\right)={\left(3x\right)}^2+2\\ =9x^2+2\end{array}$

Now, the graph of the functions are,

  

Interpretation:

The graph of $g\left(x\right)$ is scale down by 9 unit compared to the graph of $f\left(x\right)$ .

(c)

To find: How the multiplying factor changes a graph

The multiplication of a constant change the graph of the quadratic function.

Explanation:

The multiplication of a constant to a function can shift the original function or scales the function.

Hence, the multiplication of a constant change the graph of the quadratic function.