# What is the domain and range of g(x)=abs(2x-8)+1?

Nov 10, 2015

The domain is the range of $x$ values that can be inputted and the range is the set of possible values $g \left(x\right)$ can output. Thinking logically about the equation will get the answer.

#### Explanation:

The domain is the range of values of $x$ we could input into the equation. If we think logically about the equation is there any part of it that would produce an undefined answer? No there is not.

Therefore the domain is all real values of $x$, expressed as $x \in \mathbb{R}$

The range is the set of values that $g$($x$) can produce. If we think about it logically again since their is a modulus included then we can have no negative results for $2 x - 8$ . The lowest value we can produce for this part of the equation is 0 if $x$ were 4. This means the lowest value the whole equation can resolve to is 1.

This means the range of the equation is $g \left(x\right) \ge 1$.