Question

The function h(x) is defined as shown.

h(x) = StartLayout Enlarged left-brace 1st row 1st column x + 2, 2nd column x less-than 3 2nd row 1st column negative x + 8, 2nd column x greater-than-or-equal-to 3 EndLayout

What is the range of h(x)?

–∞ < h(x) < ∞
h(x) ≤ 5
h(x) ≥ 5
h(x) ≥ 3

Answer 1

For x < 3: h(x) = x + 2 < 3 + 2 = 5, so values are < 5 (down to −∞).
For x ≥ 3: h(x) = −x + 8 ≤ −3 + 8 = 5, and equals 5 at x = 3.

Thus the range is (−∞, 5], i.e. h(x) ≤ 5.