10
QuizMultiple Choice

Translations of Exponential Functions — Quiz

Question 10 • Algebra: Concepts and Connections

What is the range of f of x is equal to 3 to the x th power plus 9 ?

Answer
A
start set y such that y is less than 3 end set
B
start set y such that y is less than 9 end set
C
start set y such that y is greater than 9 end set
D
start set y such that y is greater than 3 end set

Explanation

For every real value of x, 3^x is positive, so 3^x + 9 is always greater than 9. As x decreases, 3^x can get arbitrarily close to 0, so the function’s outputs can get arbitrarily close to 9 without reaching it. Thus the range is the set of y-values greater than 9, choice D.

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