Chapter 1.4, Problem 72E

To determine

To find the $x$ intercepts of the given graph $y=f(x-3)$

Answer to Problem 72E

  $x=-1,x=-6$

Explanation of Solution

Given:

The graph of $y=f(x)$ has $x$ intercepts at $x=2$ and $x=-3$

Calculation:

Consider $f(x)=x.$

Given that the intercepts of $x$ are $x=2$ and $x=-3.$

So, if $f(x)=x,$ then $f(x-3)=x-3.$

For $x=2,$

  $\begin{array}{l}f(x-3)=x-3\\ \Rightarrow f(2-3)=-1\end{array}$

For $x=-3,$

  $\begin{array}{l}f(x-3)=x-3\\ \Rightarrow f(-3-3)=-6\end{array}$

Conclusion:

Therefore, the $x$ intercepts of $y=f(x-3)$ are $x=-1,x=-6$