# Thread: domain and range of a absolute value function

1. ## domain and range of a absolute value function

Hey

Having some trouble with this one.

Find the domain and range of $\displaystyle f(x) = -2|-2+x|$

Thanks

2. Originally Posted by smplease
Hey

Having some trouble with this one.

Find the domain and range of $\displaystyle f(x) = -2|-2+x|$

Thanks
the domain is all $\displaystyle x \in \mathbb{R}$

to find the range,. consider the case when $\displaystyle -2+x \geq 0$ and $\displaystyle -2+x < 0$

good luck

Did you make a sketch?

Find the domain and range of: .$\displaystyle f(x) = -2|-2+x|$

We have: .$\displaystyle f(x) \:=\:-2|x-2|$

You should know the graph of: .$\displaystyle f(x) \:=\:|x|$
. . It is a $\displaystyle \vee$ with its vertex at the origin.

The graph of: .$\displaystyle f(x) \:=\:|x-2|$ .is the previous graph moved 2 units to the right.

The graph of: .$\displaystyle f(x) \:=\:-2|x-2|$ .is the previous graph
. . reflected over the $\displaystyle x$-axis and is "steeper".

Hence, the graph of $\displaystyle f(x) \:=\:-2|x-2|$ looks like this:
Code:
            |
|   2
- - - + - * - - - -
|  / \
| /   \
|/     \
/       \
/|        \
|

Got it?