Question

The graphs of f(x) = 5x and its translation, g(x), are shown on the graph.

On a coordinate plane, 2 exponential functions are shown. f (x) approaches y = 0 in quadrant 2 and increases into quadrant 1. It crosses the y-axis at (0, 1) and goes through (1, 5) and (2, 25). g (x) approaches y = negative 10 in quadrant 2 and increases into quadrant 1. It goes through (0, negative 9), (1, negative 5), (2, 15).

What is the equation of g(x)?

g(x) = 5x – 9
g(x) = 5x – 10
g(x) = 5x – 9
g(x) = 5x – 10

Answer 1

The function is g(x) = 5^x − 10.

Reason: f(x)=5^x has horizontal asymptote y=0; shifting down 10 gives asymptote y=−10, so g(x)=5^x−10. Check: g(0)=1−10=−9, g(1)=5−10=−5, g(2)=25−10=15.