18
QuizMultiple Choice

Square Root and Absolute Value Functions — Test

Question 18 • Algebraic Reasoning

Consider the functions f of x is equal to 3 x squared , g of x is equal to 1 over 3 x , and h of x is equal to 3 x Which statements accurately compare the domain and range of the functions? Choose two correct answers.

Answer
A
The range of all three functions is all real numbers.
B
The range of f of x and h of x is all real numbers, but the range of g of x is all real numbers except 0 .
C
All of the functions have a unique range.
D
The domain of all three functions is all real numbers.
E
The domain of f of x and h of x is all real numbers, but the domain of g of x is all real numbers except 0 .

Explanation

For f(x) = 3x² and h(x) = 3x, any real number can be used as an input, so their domains are all real numbers. For g(x) = 1/(3x), x cannot be 0 because that would make the denominator 0, so its domain excludes 0; this makes E correct. Their ranges are distinct: f has range [0, ∞), g has range all real numbers except 0, and h has range all real numbers, so C is correct.

AI-written and checked against the verified answer.

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