5
QuizMultiple Choice

Linear Functions — Quiz

Question 5 • Algebraic Reasoning

If f of x is a linear function and the domain of f of x is the set of all real numbers, which statement cannot be true?

Answer
A
The graph of f of x has exactly one x -intercept.
B
The graph of f of x has zero x -intercepts.
C
The graph of f of x has infinitely many x -intercepts.
D
The graph of f of x has exactly two x -intercepts.

Explanation

A linear function has the form f(x) = mx + b. If m is nonzero, its graph crosses the x-axis exactly once; if m = 0, it has either no x-intercepts or infinitely many, depending on whether b is nonzero or zero. It cannot have exactly two x-intercepts, so the statement that cannot be true is “The graph of f(x) has exactly two x-intercepts.”

AI-written and checked against the verified answer.

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