Chapter 3.5, Problem 2E

Solution

a.

To Explain: The changes in graph of $y=\sqrt{x}$ if $a=-3$

  $y=\sqrt{x}$ is the graph of $y=a\sqrt{x-h}+k.$

Given information:

The given square root function is $y=\sqrt{x}$ and the graph formation function $y=a\sqrt{x-h}+k.$ .

and $a=-3$ is also given.

Concept used:

The graph of the function $y=a\sqrt{x-h}+k$ is reflected to x axis if $a<0$ .

Explanations:

Here the function is $y=\sqrt{x}$ and $a=-3$ .

If $a=-3$ then graph will be reflected to $x$ axis.

b.

To Explain: The changes in graph of $y=\sqrt{x}$ if $h=2$

  $y=\sqrt{x}$ is the graph of $y=a\sqrt{x-h}+k.$

Given information:

The given square root function is $y=\sqrt{x}$ and the graph formation function $y=a\sqrt{x-h}+k.$ .

and $h=2$ is also given.

Concept used:

The graph of the function $y=a\sqrt{x-h}+k$ if $h>0$ the graph is horizontally translated right by $h$ units.

Explanations:

Here the function is $y=\sqrt{x}$ and $h=2$ .

If $h=2$ then graph will be horizontally translated right by $2$ units.

c.

To Explain: The changes in graph of $y=\sqrt{x}$ if $k=4$

  $y=\sqrt{x}$ is the graph of $y=a\sqrt{x-h}+k.$

Given information:

The given square root function is $y=\sqrt{x}$ and the graph formation function $y=a\sqrt{x-h}+k.$ .

and $k=4$ is also given.

Concept used:

The graph of the function $y=a\sqrt{x-h}+k$ if $k>0$ the graph will move vertically up by $k$ units.

Explanations:

Here the function is $y=\sqrt{x}$ and $k=4$ .

If $k=4$ then graph will move vertically up by $4$ units.

d.

To Explain: The changes in graph of $y=6\sqrt[3]{x}$ from the parent function.

Given information:

The given square root function is $y=6\sqrt[3]{x}$ .

Concept used:

The graph of the function $y=a\sqrt{x-h}+k$ if $k>0$ if $\left|a\right|>1$ then the graph is vertically stretched by $\left|a\right|$ units.

Explanations:

Here the function is $y=6\sqrt[3]{x}$ and $a=6$ .

If $a=6,\left|6\right|>1$ then graph will move vertically stretched by $6$ units.