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

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#### Explanation

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#### Explanation:

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2
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 $- 3 x$ 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 $\left(0 , 0\right)$, it moves up by $2$.

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

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