Answer :
Options:
- 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.
Answer:
(C)The graph of f(x) has exactly two x-intercepts.
Step-by-step explanation:
Given a linear function f(x)=ax+b where the domain of f(x) is the set of all real numbers, x.
(A)If f(x)=y, the graph of f(x) will have zero x-intercepts except at y=0 which is the equation of the x-axis.
(B)A linear function can only intersect the x-axis at exactly one point.
(D)When the linear function is f(x)=0, all points of x are x-intercepts of f(x). Therefore f(x) will have infinitely many x-intercepts at this point.
However:
A straight line cannot intersect the x-axis twice, therefore the graph of f(x) cannot have two x-intercepts.
The statement which cannot be true is Option C.