# Given f(x) = |x - 1|, what is the range of f(x)?

Sep 6, 2016

Range is y ≥ 0.

#### Explanation:

Start by finding the vertex of the graph.

In $y = a | b \left(x - p\right) | + q$, the vertex is at $\left(p , q\right)$.

Hence, our vertex is at $\left(1 , 0\right)$.

Now, the other element that will influence the range is the direction of opening. The rule is if $a$ in $y = a | b \left(x - p\right) | + q$ is positive, than the graph opens up. Similarly, if a is negative, the graph opens down.

Here, $a = 1$, so the graph opens up.

Our range will thus be y ≥ 0.

Hopefully this helps!