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Nonlinear functions SAT question

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

  • For the first curve: 
    • Moving from left to right:
      • The curve passes from quadrant 2 to quadrant 1.
      • In quadrant 2, the curve trends up gradually to point (0 comma 3).
      • In quadrant 1, the curve trends up sharply.
    • As x increases, the curve approaches the line x equals 4.
    • As x decreases, the curve approaches the line y equals 1.
    • The curve passes through the following points:
      • (negative 3 comma 2)
      • (0 comma 3)
  • For the second curve: 
    • Moving from left to right:
      • The curve is in quadrant 4.
      • In quadrant 4, the curve trends up sharply.
    • As x increases, the curve approaches the line y equals 1.
    • As x decreases, the curve approaches the line x equals 4.
    • The curve passes through the following point:
      • (6 comma negative 4)

The graph of  is shown in the xy-plane. What is the value of ?

ExplanationShow

Choice D is correct. Because the graph of  is shown, the value of  is the value of on the graph that corresponds with . When , the corresponding value of is . Therefore, the value of  is .

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

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