How do you graph y=|-3x|+2?

1 Answer
Feb 13, 2018

Below.

Explanation:

Here's what the graph y= |x| looks like, the base equation without any transformations. Let's call this the base function.

graph{|x| [-10, 10, -5, 5]}

Now let's add the -3.

The use of the "||" brackets around the -3x makes the function an absolute value function . That means for every x value you put in, the y value you receive is the same but positive. So, because this equation is |-3|, these brackets make it so you can ignore the negative completely.

Adding the 3 in front of the x squishes the graph so that every y value is 3 times the base function. (Sort of takes a bit to understand that multiplying the way makes the graph squished).

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

Lastly, the +2 is a vertical shift, which means that you move the graph up by 2, so instead of starting the V shape at the (0,0), it moves up by 2.

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