Question

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

Answer 1

Range is `y ≥ 0`.

Explanation:

Start by finding the vertex of the graph.

In `y = a|b(x - p)| + q`, the vertex is at `(p,q)`.

Hence, our vertex is at `(1, 0)`.

Now, the other element that will influence the range is the direction of opening. The rule is if `a` in `y = a|b(x - p)| + 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!