Answer
Option C. Let’s break it down step by step: The function is f(x) = -0.08x(x^2 – 11x + 18). To find the x-intercepts, we need to factor the quadratic part (x^2 – 11x + 18). We look for two numbers that multiply to 18 and add up to -11, which are -9 and -2. Thus, we can rewrite it as (x – 9)(x – 2), giving us f(x) = -0.08x(x – 9)(x – 2). Setting f(x) to zero: -0.08x(x – 9)(x – 2) = 0 leads us to three solutions: x = 0, x = 2, and x = 9. These x-intercepts are (0, 0), (2, 0), and (9, 0), confirming that they do not repeat. Therefore, the graph crosses the x-axis at these points, making option C the correct choice. The relevant graph is provided below.
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