Question

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases from quadrant 2 into quadrant 1. It crosses the y-axis at (0, 1).
Which function is a shrink of the exponential growth function shown on the graph?

f(x) = 2(3)x
f(x) = One-half(3)x
f(x) = 2(one-third) Superscript x
f(x) = One-half (one-third) Superscript x

Answer 1

The base graph is an exponential growth (base > 1) with y-intercept 1, so a vertical shrink is a factor between 0 and 1 multiplying that growth function. The only option that is a vertical shrink of a growth function is

f(x) = (1/2)·3^x.

(2·3^x is a vertical stretch; any (1/3)^x is exponential decay, not the given growth.)