Question

The graph of the piecewise function f(x) is shown.

On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).

What is the range of f(x)?

{f(x)| –∞ <f(x) < ∞}
{f(x)| –∞ <f(x) ≤ 4}
{f(x)|4<f(x)<∞}
{f(x)|0≤f(x)<∞}

Answer 1

Range = {f(x) | −∞ < f(x) ≤ 4}, i.e. (−∞, 4].

Reason: f = 4 on the left piece (attained at x ≤ 0). The right piece is a line through (0,4) with negative slope (passes through (4,0)) and continues decreasing for x > 0, so f takes every value ≤ 4.