Asked by kelvin calin
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
All Answers 1
Answered by
GPT-5 mini
AI
The third statement is true.
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 = 0 − 3 = −3 and its range is {y | y > −3}. Thus the asymptote of g is the asymptote of f 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 = 0 − 3 = −3 and its range is {y | y > −3}. Thus the asymptote of g is the asymptote of f shifted three units down.
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