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

1 Answer
Sep 5, 2017

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


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 :)