Question

How do you graph the equation `y=|x+2|+3`?

Answer 1

The absolute value changes of sign, when it's content `< 0`.
So let's write that down:
`x+2 < 0 <=> x < -2`
So now we know that it will change the sign (negative) when `x<-2`
It's best to treat a function with an absolute value as two functions.

• `x > -2 => y = x+2+3 <=> y = x+5`
• `x < -2 => y = -(x+2)+3 <=> y = -x-2+3 <=> y = -x + 1`

See how I added the minus sign when `x<-2`?

If you now graph both of these functions on one graph, you will have your function. You do have to remember that the first function only exists when `x > -2`, and that the second function only exists when `x < -2`.