Question

How do you graph `Y=abs [-3x] + 2`?

Answer 1

List the transformations performed and apply it to the base function.

Explanation:

First off, it's a lowercase `y`.

This function is an absolute value.

There are a total of 3 transformations being done to the function.

1. Horizontal compression. With the `3` inside the absolute value, it affects the horizontal component of the function. It compresses the function by a factor of `1/3`.
2. The vertical translation. With a positive value of `2` outside the absolute value, it causes a vertical shift in the function.
3. Reflection on `y`-axis. This honestly doesn't matter because it's a reflection off of the `y`-axis, but it's an absolute value, so it doesn't really alter the image - but I say it anyways to prove that the transformation occurred.

In order to graph this, we must consider the base function of `f(x)=|x|`. Now we apply the transformations we listed above.

You should get something like this:

graph{|-3x|+2 [-10, 10, -5, 5]}

Hope this helps :)