Final answer:
The graph of a linear function cannot have exactly two x-intercepts because a linear function, represented by a straight line, can only intersect the x-axis at one point or be parallel (with zero or infinitely many x-intercepts).
Step-by-step explanation:
A linear function such as f(x) with the domain of all real numbers is represented graphically by a straight line. For a linear function, we can encounter different scenarios related to its intersections with the x-axis:
- If the linear function is not horizontal (i.e., has a non-zero slope), it will cross the x-axis at exactly one point, signifying exactly one x-intercept.
- If the linear function is horizontal (i.e., has a zero slope), it may either coincide with the x-axis (infinitely many x-intercepts) or it will not touch the x-axis at all (zero x-intercepts), depending on its y-intercept value.
Considering these points, the graph of a linear function cannot have exactly two x-intercepts because a straight line cannot bend to touch the x-axis twice. Therefore, the statement The graph of f(x) has exactly two x-intercepts cannot be true.