AnswersHigh School Math 2 ATranslations of Exponential FunctionsQuestion 10
10
QuizMultiple Choice

Translations of Exponential Functions

Question 10 • High School Math 2 A

f(x) = 7x g(x) = 7x + 6

Answer
A
The domain of g(x) is {x | x > 6}, and the domain of f(x) is {x | x > 0}.
B
The domain of g(x) is {y | y > 0}, and the domain of f(x) is {y | y > 6}.
C
The asymptote of g(x) is the asymptote of f(x) shifted six units down.
D
The asymptote of g(x) is the asymptote of f(x) shifted six units up.

Explanation

Since g(x) = 7x + 6 = f(x) + 6, the graph of g is the graph of f shifted six units up. A vertical shift moves a function’s horizontal asymptote up by the same amount, so g’s asymptote is f’s asymptote shifted six units up. The domain choices are incorrect because both functions are defined for every real x.

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