Question

Which function represents a vertical stretch of an exponential function?
f (x) = 3 (one-half) Superscript x
f (x) = one-half (3) Superscript x
f (x) = (3) Superscript 2 x
f (x) = 3 Superscript (one-half x)

Answer 1

f(x) = 3(1/2)^x.

Reason: a vertical stretch multiplies the whole function by a constant > 1. Here the factor 3 outside (1/2)^x stretches the graph vertically by 3.
- f(x) = (1/2)·3^x is a vertical shrink (factor 1/2).
- f(x) = 3^{2x} and f(x) = 3^{(1/2)x} change the exponent (horizontal compression/stretch), not a vertical stretch.