15
QuizMultiple Choice

Exponential Functions with Radical Bases — Quiz

Question 15 • Algebra I

How are the graphs of the functions f of x is equal to square root of 16 to the x th power and g of x is equal to cube root of 64 to the x th power related?

Answer
A
The function g of x decreases at a faster rate.
B
The function g of x has a greater initial value.
C
The functions f of x and g of x are equivalent.
D
The function g of x increases at a faster rate.

Explanation

Rewrite each radical as an exponent: f(x) = √(16^x) = 16^(x/2) = 4^x, and g(x) = ∛(64^x) = 64^(x/3) = 4^x. Since both functions equal 4^x for every value of x, their graphs are identical. The functions are equivalent.

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