Chapter 10.1, Problem 52E

(a)

To determine

To find the value of graph be identical.

Answer to Problem 52E

  $a=\frac{1}{8}$

Explanation of Solution

Given information: $f\left(x\right)=8a\sqrt{x}$

Formula Used: Square root function

Calculation:

  $f\left(x\right)=8a\sqrt{x}$

The value of a will the graph of f be identical to the graph of parent square root function.

When $a=\frac{1}{8}$

So,

  $f\left(x\right)=8\times \frac{1}{8}\times \sqrt{x}$

Hence,

  $f\left(x\right)=\sqrt{x}$

(b)

To determine

To find the value of graph be vertical stretch.

Answer to Problem 52E

  $a=\frac{1}{4}$

Explanation of Solution

Given information: $f\left(x\right)=8a\sqrt{x}$

Formula Used: Square root function

Calculation:

  $f\left(x\right)=8a\sqrt{x}$

The value of a will the graph of f be vertical stretch to the graph of parent square root function.

When $a=\frac{1}{4}$

So,

  $f\left(x\right)=8\times \frac{1}{4}\times \sqrt{x}$

Hence,

  $f\left(x\right)=2\sqrt{x}$

  

(c)

To determine

To find the value of graph be vertical shrink.

Answer to Problem 52E

  $a=-\frac{1}{16}$

Explanation of Solution

Given information: $f\left(x\right)=8a\sqrt{x}$

Formula Used: Square root function

Calculation:

  $f\left(x\right)=8a\sqrt{x}$

The value of a will the graph of f be vertical shrink to the graph of parent square root function.

When $a=-\frac{1}{16}$

So,

  $f\left(x\right)=8\times \left(-\frac{1}{16}\right)\times \sqrt{x}$

Hence,

  $f\left(x\right)=-\frac{1}{2}\sqrt{x}$