Question

Which function has a range of y < 3?
y = 3 (2) Superscript x
y = 3 (3) Superscript x
y = negative (2) Superscript x Baseline + 3
y = (2) Superscript x Baseline minus 3

Answer 1

y = -2^x + 3.

Reason: 2^x > 0 for all x, so -2^x < 0 and -2^x + 3 < 3 for all x. The horizontal asymptote is y = 3 (approached from below), so the range is (-∞, 3), i.e. y < 3.