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Advanced Math Difficulty: Medium

The graph of $y = f (x)$ is shown, where the function $f$ is defined by $f (x) = a x^{3} + b x^{2} + c x + d$ and $a$ , $b$ , $c$ , and $d$ are constants. For how many values of $x$ does $f left parenthesis x right parenthesis equals 0$ ?

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Explanation

Choice C is correct. If a value of $x$ satisfies $f left parenthesis x right parenthesis equals 0$ , the graph of $y = f (x)$ will contain a point $left parenthesis x comma 0 right parenthesis$ 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 $f left parenthesis x right parenthesis equals 0$ .

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.