SAT question cc6ccd71 (Nonlinear Functions)

Question

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 ( x ) = 0 ?

College Board · Accepted Answer

The correct answer is C. Choice C is correct. If a value of x satisfies f ( x ) = 0 , the graph of y = f ( x ) 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 .

CookSAT · Answer

Note: Graph f and count its x-intercepts; the three factors give crossings at x=-1, 4, and 7.

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question cc6ccd71: Nonlinear Functions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong