Chapter 1.2, Problem 35E

To determine

To verify: The claim of friend regarding order of transformations.

Answer to Problem 35E

Friend is incorrect.

Explanation of Solution

Given information: Order of transformations is to be discussed.

Calculation:

When considering transformations, order is important as changing the order of transformations can give varying results,

For example,

  $f(x)=x$

Reflecting over $x-axis$ ,

  $\begin{array}{l}h(x)=-f(x)\\ \\ h(x)=-x\end{array}$

Translating $5units$ down,

  $\begin{array}{l}g(x)=h(x)-5\\ \\ g(x)=-x-5\end{array}$

Now applying the same transformations but in reverse order,

Translating $5units$ down,

  $\begin{array}{l}h(x)=f(x)-5\\ \\ h(x)=x-5\end{array}$

Reflecting over $x-axis$ ,

  $\begin{array}{l}g(x)=-h(x)\\ \\ g(x)=-(x-5)\\ \\ g(x)=-x+5\end{array}$

Transformed function is different after altering the order of transformations,

Thus, friend is incorrect.