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`