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Advanced Math / Nonlinear functions Difficulty: Medium
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The graph of y=fx is shown, where the function f is defined by fx=ax3+bx2+cx+d and a , b , c , and d are constants. For how many values of x does fx=0?

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Explanation

Choice C is correct. If a value of x  satisfies f(x)=0, the graph of y=fx will contain a point x,0 and thus touch the x-axis. Since there are 3 points at which this graph touches the x-axis, there are 3 values of x for which f(x)=0.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.