We want to describe how to transform the to the graph of the given .
To do so, we need to consider two possible transformations.
- Horizontal stretches and shrinks
Let's consider them one at the time.
Horizontal stretch or shrink
We have a horizontal stretch
is multiplied by a number greater than
is multiplied by a number whose is less than
one, a horizontal shrink
will take place.
In the given exercise, is multiplied by Therefore, the previous graph will be horizontally shrunk by a factor of
Whenever is multiplied by a negative number, we will have a of the graph across the -axis.
Note how each -coordinate stays the same, and how each -coordinate changes its sign.
Let's now graph the given function and the parent function on the same coordinate grid.
Finally, let's summarize all the transformations of the graph of
- A horizontal shrink by a factor of
- Reflection in the -axis