What would the graph look like with this equation?  y = |x+3| -2 

Expert Answers
lemjay eNotes educator| Certified Educator


Note that a graph of a function with absolute value is V-shaped.

To determine the graph of it, consider the graph of function y=|x| which is :

Then, apply the transformation of axis. So isolate the expression of with absolute value in the given equation.  To do so, add both sides by 2.

`y = |x+3|-2`



Now, consider each side of the equation. 

For  y+c, it means that the original graph is shifted c units down. So, move the graph of  `y=|x|`    two (2) units down.

And for x + c, it means that the original graph is shifted c units to the left. So, move the graph of `y=|x|`  three (3) units to the left.

Hence, the graph of `y=|x+3|-2` is:

embizze eNotes educator| Certified Educator

Graph y=|x+3|-2:

Given the base function y=|x|, y=|x-h|+k will be translated h units left/right (right if h>0, left if h<0) and k units up/down (up if k>0, down if k<0).

So the graph of y=|x+3|-2 will be the graph of y=|x| shifted 3 units left (Note that h=-3; x-(-3)=x+3) and 2 units down. The vertex will be at (-3,-2), the graph opens up, and the sides have slope of `+-1` .

The graph of y=|x| in black and y=|x+3|-2 in red: