Question

how do I use a function to write the transformation

Answer 1

For this exercise you need to remember the following Transformation Rules for functions:

1. If:

$f(x)+k$

Then the function is translated "k" units up.

2. If:

$f(x)-k$

Then the function is translated "k" units down.

3. If:

$-f(x)$

Then the function is reflected across the x-axis.

4. If:

$f(-x)$

The function is reflected across the y-axis.

You have the following function f(x):

$f\mleft(x\mright)=2^{x-3}+1$

Based on the above, you know that if it is reflected across the x-axis and translated 5 units up, the function g(x) is:

$\begin{gathered} g(x)=-(2^{x-3}+1)+5 \\ g(x)=-2^{x-3}-1+5 \\ g(x)=-2^{x-3}+4 \end{gathered}$

The answer is:

$g(x)=-2^{x-3}+4$