Question

Which function is graphed below?

On a coordinate plane, an exponential decay function is shown. The curve starts in quadrant 2 and decreases into quadrant 1. It crosses the y-axis at (0, 3) and approaches y = 0 in quadrant 1.
y = one-third (3) Superscript x
y = 3 (one-third) Superscript x
y = (one-half) Superscript x Baseline + 2
y = (2) Superscript x Baseline minus 1

Answer 1

y = 3(1/3)^x

Reason: the graph is exponential decay with horizontal asymptote y = 0 and y-intercept (0,3). y = 3(1/3)^x gives y(0) = 3 and decays as x increases. The other choices either have the wrong y-intercept or a nonzero horizontal asymptote or are exponential growth.