Going Backwards with transformations

Hi class, This is Greg! A few classes ago, we learned about going backwards with transformations. Today I will be doing a re-cap of everything we covered that day.

In order to go backwards, you must do all the steps in reverse order. So in this case, you first figure out the transformations. Then move along with the stretches and reflections.

Example 1: The function  y=f(x-2)+3 is graphed below. How would you sketch a graph of the function f(x)?

Keep in mind.

Outside the function à affects the y-values à the effect is the same.

Inside the function à affects the x-values à the effect is the opposite.

But since you’re working backwards, the effect would be opposite.

First off, instead of adding 3 to the y-value of the coordinates (+3) you must subtract 3 instead. For the x-value (-2) you must subtract 2 instead of adding 2.

Sketch the new graph to represent f(x) using the new coordinates.

Example 2: (No Graph)

The function y=3f(-2[x-2])-2 = (-2,4), Then what is f(x)?

For this question, you must figure out the new coordinates for the function f(x).

First you start of with the transformations, and then move on with the stretches and reflections. For stretches you would originally multiply, but in this case you would have to do the opposite and divide.

For the x-value (-2) you must subtract 2 (=-4) Then divide it by -½ (=8).

For the y-value (4) you must add 2 (=6) Then divide it by 3 (=2)

f(x)= (8,2)

HAVE A GREAT DAY!!!