Question

f(x) = (two-fifths) Superscript x

g(x) = (two-fifths) Superscript x – 3

Which statement about f(x) and its translation, g(x), is true?

The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.

Answer 1

"The asymptote of g(x) is the asymptote of f(x) shifted three units down."

Reason: f(x) = (2/5)^x has horizontal asymptote y = 0 and range {y | y > 0}. g(x) = (2/5)^x − 3 is f shifted down 3, so its asymptote is y = −3 and its range is {y | y > −3}.