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

1 Answer
Sep 6, 2016

Answer:

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!