新SAT数学OG真题Test04 Section4 Q12
In the xy-plane, the graph of function ff has x-intercepts at-3, -1, and 1. Which of the following could define ff?
A . f(x)=(x−3)(x−1)(x+1)
B . f(x)=(x−3)(x−1)2
C . f(x)=(x−1)(x+1)(x+3)
D . f(x)=(x+1)(x+1)(x+3)
Choice С is correct. All of the given choices are polynomials. If the graph of a polynomial function ff in the xy-plane has an x-intercept at b, then(x−b) must be a factor off(х). Since -3, -1, and 1 are each x-intercepts of the graph of f, it follows that (x+3)), (x+1)), and(x−1) must each be a factor of f(x). The factored polynomial function in choice С is the only polynomial given with these 3 factors.
Choices A, B, and D are incorrect because they do not contain all three factors that must exist if the graph of the polynomial function ff has x-intercepts at -3, -1, and 1.
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