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Nonlinear functions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

  • 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  is shown, where the function is defined by and , , , and are constants. For how many values of does ?

ExplanationShow

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

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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