Chapter 11.2, Problem 42E

To determine

To describe: the transformation that have taken place and identify the new location of the asymptotes by using the parentgraphs.

Answer to Problem 42E

The first graph is translation of second graph of 3 units down.

Explanation of Solution

Given:

The graph of $f\left(x\right)=\frac{1}{x}$ and $f\left(x\right)=\frac{1}{x+3}$ .

Calculation:

According to the given graph in the question:

Thegraph of $f\left(x\right)=\frac{1}{x+3}$ is translated the 3 units left.

Thus, the vertical asymptote is $x=3$ and the horizontalasymptote is $y=0$ , is unchanged because there is no change horizontally.

Now, the graph of $f\left(x\right)=\frac{1}{x+3}$ and $f\left(x\right)=\frac{1}{x}$ is given below

Hence, the first graph is translation of second graph of 3 units down.