Chapter 11.2, Problem 23E

a.

To determine

To describe: the relation between the graphs of $y=6^x$ and $y=6^x+4$ . Then use a graphing calculator to check the descriptions

Answer to Problem 23E

The first graph is translation of second graph with 4 units up.

Explanation of Solution

Given:

Thegraphs of $y=6^x$ and $y=6^x+4$ .

Calculation:

According to the given graph in the question:

Thegraph of $y=6^x+4$ is obtained by the first graph when shifting the first graphof $y=6^x$ upfour units.

Now, using a graphing calculator to check the descriptions:

Hence,the first graph is translation of second graph with 4 units up.

b.

To determine

To describe: the relation between the graphs of $y=-3^x$ and $y=3^x$ . Then use a graphing calculator to check the descriptions

Answer to Problem 23E

Thegraph of $y=-3^x$ is a reflection of the graphof $y=3^x$ across x-axis.

Explanation of Solution

Given:

The graphs of $y=-3^x$ and $y=3^x$ .

Calculation:

According to the given graph in the question:

Thegraph of $y=-3^x$ is a reflection of the graphof $y=3^x$ across x-axis.

Now, using a graphing calculator to check the descriptions:

Hence, thegraph of $y=-3^x$ is a reflection of the graphof $y=3^x$ across x-axis.

c.

To determine

To describe: the relation between the graphs of $y=7^{-x}$ and $y=7^x$ . Then use a graphing calculator to check the descriptions

Answer to Problem 23E

Thegraph of $y=7^{-x}$ is a reflection of the graphof $y=7^x$ across y-axis.

Explanation of Solution

Given:

The graphs of $y=7^x$ and $y=7^{-x}$ .

Calculation:

According to the given graph in the question:

Thegraph of $y=7^{-x}$ is a reflection of the graphof $y=7^x$ across y-axis.

Now, using a graphing calculator to check the descriptions:

Hence, thegraph of $y=7^{-x}$ is a reflection of the graphof $y=7^x$ across y-axis.

d.

To determine

To describe: the relation between the graphs of $y=2^x$ and $y={\left(\frac{1}{2}\right)}^x$ . Then use a graphing calculator to check the descriptions

Answer to Problem 23E

Thegraph of $y={\left(\frac{1}{2}\right)}^x={\left(2^{-1}\right)}^x$ is a reflection of the graphof $y=2^x$ across y-axis.

Explanation of Solution

Given:

The graphs of $y=2^x$ and $y={\left(\frac{1}{2}\right)}^x$ .

Calculation:

According to the given graph in the question:

Thegraph of $y={\left(\frac{1}{2}\right)}^x={\left(2^{-1}\right)}^x$ is a reflection of the graphof $y=2^x$ across y-axis.

Now, using a graphing calculator to check the descriptions:

Hence, thegraph of $y={\left(\frac{1}{2}\right)}^x={\left(2^{-1}\right)}^x$ is a reflection of the graphof $y=2^x$ across y-axis.