The function f is defined above. Which of the following is NOT an x -intercept of the graph of the

Question

The function f is defined above. Which of the following is NOT an x -intercept of the graph of the function in the xy -plane?

Accepted Answer

Choice B is correct. The graph of the function f in the xy -plane has x -intercepts at the points , where . Substituting 0 for in the given equation yields . By the zero product property, if , then , , or . Solving each of these linear equations for x , it follows that , , and , respectively. This means that the graph of the function f in the xy -plane has three x -intercepts: , , and . Therefore, isn&rsquo;t an x -intercept of the graph of the function f . Alternate approach: Substitution may be used. Since by definition an x -intercept of any graph is a point in the form where k is a constant, and since all points in the options are in this form, it need only be checked whether the points in the options lie on the graph of the function f . Substituting for x and 0 for in the given equation yields , or . Therefore, the point doesn&rsquo;t lie on the graph of the function f and can&rsquo;t be an x -intercept of the graph. Choices A, C, and D are incorrect because each of these points is an x -intercept of the graph of the function f in the xy -plane. By definition, an x -intercept is a point on the graph of the form , where k is a constant. Substituting for x and 0 for in the given equation yields , or . Since this is a true statement, the point lies on the graph of the function f and is an x -intercept of the graph. Performing similar substitution using the points and also yields the true statement , illustrating that these points also lie on the graph of the function f and are x -intercepts of the graph.

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