7
QuizMultiple Choice

Translations of Exponential Functions

Question 7 • High School Math 2 A

What are the domain, range, and asymptote of h(x) = (1.4)x + 5?

Answer
d
domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
d
domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
d
domain: {x | x > –5}; range: {y | y is a real number}; asymptote: y = –5
d
domain: {x | x is a real number}; range: {y | y > –5}; asymptote: y = –5

Explanation

Interpreting the function as the exponential function h(x) = (1.4)^x + 5, every real x is allowed, so the domain is all real numbers. Since (1.4)^x is always positive, h(x) is always greater than 5. As x decreases, (1.4)^x approaches 0, so the horizontal asymptote is y = 5; this matches choice A.

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