Question

How do you graph `y=|x+4|-2`?

Answer 1

The graph should look like this: graph{|x+4|-2 [-10, 10, -5, 5]}

Explanation:

There is a way to mathematically calculate the different situations to graph this, but I will use the simpler way for this one.

First, remember that if `y=f(x)` and `f(x)=x`,
`f(x+y)` will be the same as moving the graph of `f(x)=x` right y times if y is negative and to the left y times if y is positive in the function.
Therefore, we first graph of `y=|x|`
graph{|x| [-10, 10, -5, 5]}
Then, we shift the function to the left four spaces.
graph{|x+4| [-10, 10, -5, 5]}
Now, also remember that when we have `f(x)+y` we move the graph up y times if y is positive and down y times if y is negative in the function.

Therefore, we shift the function `f(x)=x+4` down two spaces.
graph{|x+4|-2 [-10, 10, -5, 5]}
You graphed the function!