Question

The graph of f(x) has zero x-intercepts.

The graph of f(x) has exactly one x-intercept.
The graph of f(x) has exactly two x-intercepts.
The graph of f(x) has infinitely many x-intercepts.

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

Answer 1

The graph of f(x) has exactly two x-intercepts.

Answer 2

option b.

The graph of f(x) has exactly one x-intercept.

Explanation:

Given that the function f(x) is a linear function defined for all real values of x.

Thus graph of f(x) would be a straight line cutting x axis exactly at one point.

Hence f(x) cannot have two intercepts or infinitely many intercepts.

zero intercept is possible only if the function is constant as y=a

Thus out of the four options given the correct option is

option b.

The graph of f(x) has exactly one x-intercept.