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2.1 Nonlinear Functions - Polynomial end behavior and turning points
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  • In quadrant 2 the curve falls sharply to cross the x axis at point (negative 1 comma 0).
  • In quadrant 3 the curve falls sharply to cross the y axis at point (0 comma negative 5.5).
  • In quadrant 4:
    • The curve falls gradually to a relative minimum at point (1 comma negative 7).
    • The curve rises sharply to cross the x axis at point (4 comma 0).
  • In quadrant 1:
    • The curve rises sharply to a relative maximum at point (5.5 comma 3).
    • The curve falls sharply to cross the x axis at point (7 comma 0).
  • In quadrant 4 the curve falls sharply. 

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?

A.

One

B.

Two

C.

Three

D.

Four

In quadrant 2 the curve falls sharply to cross the x axis at point (negative 1

Medium-difficulty · SAT Math · Nonlinear Functions — Polynomial end behavior and turning points. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer 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.

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