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2.1 Nonlinear Functions - Function composition and evaluation
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  • Moving from left to right:
    • The curve is shown in quadrant 1.
    • The curve trends down sharply to x equals 3.
    • The curve then trends down gradually.
  • As x increases, the curve approaches the line y equals 0.
  • The curve passes through the following points:
    • (2 comma nine halves)
    • (3 comma 3)
    • (6 comma three halves)

The graph of the rational function f is shown, where y=f(x) and x≥0. Which of the following is the graph of y=f(x)+5, where x≥0?

A.

  • Moving from left to right:
    • The curve passes from quadrant 1 to quadrant 4.
    • The curve trends down sharply to x equals 3. 
    • The curve then trends down gradually.
  • As x increases, the curve approaches the line y equals negative 5.
  • The curve passes through the following points:
    • (2 comma negative one half)
    • (3 comma negative 2)
    • (6 comma negative seven halves)

B.

  • Moving from left to right:
    • The curve is shown in quadrant 1.
    • The curve trends down sharply to x equals 1. 
    • The curve then trends down gradually.
  • As x increases, the curve approaches the line y equals 0.
  • The curve passes through the following points:
    • (2 comma nine tenths)
    • (3 comma three fifths)
    • (6 comma three tenths)

C.

  • Moving from left to right:
    • The curve is shown in quadrant 1.
    • The curve trends down sharply to x equals 2. 
    • The curve then trends down gradually.
  • As x increases, the curve approaches the line y equals 0.
  • The curve passes through the following points:
    • (2 comma 7)
    • (3 comma StartFraction 14 Over 3 EndFraction)
    • (6 comma seven thirds)

D.

  • Moving from left to right:
    • The curve is shown in quadrant 1.
    • The curve trends down sharply to x equals 3. 
    • The curve then trends down gradually.
  • As x increases, the curve approaches the line y equals 5.
  • The curve passes through the following points:
    • (2 comma StartFraction 19 Over 2 EndFraction)
    • (3 comma 8)
    • (6 comma StartFraction 13 Over 2 EndFraction)

Moving from left to right: The curve is shown in quadrant 1. The curve trends down

Hard-difficulty · SAT Math · Nonlinear Functions — Function composition and evaluation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. It's given that the graph of the rational function f is shown, where y=fx and x≥0. The graph shown passes through the point 3,3. It follows that when the value of x is 3 , the value of fx is 3 . When the value of fx is 3 , the value of fx+5 is 3+5, or 8 . Therefore, the graph of y=fx+5 passes through the point 3,8. Of the given choices, choice D is the only graph that passes through the point 3,8 and is therefore the graph of y=fx+5.

Choice A is incorrect. This is the graph of y=fx-5, rather than y=fx+5.

Choice B is incorrect. This is the graph of y=fx5, rather than y=fx+5.

Choice C is incorrect and may result from conceptual or calculation errors.

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