Chapter 1, Problem 46RE

Solution

The graph of $y=f\left(x-1\right)$ .

The graph of $y=f\left(x-1\right)$ shifted by one unit right from original $y=f\left(x\right)$ .

Given:

The graph of $y=f\left(x\right)$ is

  

Concept Used:

The graph of $y=f\left(x-c\right)$ can be obtained by horizontal translation of the graph of $y=f\left(x\right)$ by c units right.

Calculation:

The graph of $y=f\left(x-1\right)$ is horizontal translation of $y=f\left(x\right)$ i by one unit right. The graph shifted from original (represented by red dotted) $y=f\left(x\right)$ as shown below,

  

Hence, the desired graph of $y=f\left(x\right)-1$ is

  

Conclusion The graph of $y=f\left(x-1\right)$ shifted by one unit right.