18
QuizMultiple Choice

Mathematical Modeling: Part Three — Test

Question 18 • Mathematics III

What are the domain and range of the function f of x is equal to 2 raised to the x plus 1 power ?

Answer
A
domain: open paren negative infinity comma infinity close paren range: open paren 0 comma infinity close paren
B
domain: open paren 0 comma infinity close paren range: open paren 2 comma infinity close paren
C
domain: open paren negative infinity comma infinity close paren range: open paren 2 comma infinity close paren
D
domain: open paren 0 comma infinity close paren range: open paren negative infinity comma infinity close paren

Explanation

The function is f(x) = 2^(x + 1). Any real number can be used for x, so the domain is all real numbers, or (−∞, ∞). Powers of 2 are always positive, and they can get arbitrarily close to 0 without reaching it, so the range is (0, ∞), matching choice B.

AI-written and checked against the verified answer.

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