Chapter 3.7, Problem 23E

To determine

To find: equations of $f\left(x\right)$ for the transformation shown in the graph.

Answer to Problem 23E

  $g\left(x\right)=-\frac{1}{x}+1$

Explanation of Solution

Given information:

  $f\left(x\right)=\frac{1}{x}$

The graph for $f\left(x\right)$ and for the function after transformation is as follows:

  

Calculation:

Look at the basic graph function of transformation shown below.

  $y=\frac{1}{x-h}+v$

Here, horizontal and vertical movement is represented by $h$ and $v$ respectively.

The subtraction $(-)$ is down for moving down or moving left. Addition $(+)$ is used form moving up or right. The horizontal movements occur within x-operations $\left(x-h\right)$ .

From the graph, it is clear that the graph is mirrored around the y axis so we need to replace x with $-x$ , and the horizontal asymptote has moved 1 unit up.

Thus, the equation of transformation by $f\left(x\right)$ will be as follows:

  $g\left(x\right)=-\frac{1}{x}+1$