SAT Math Multiple Choice Question 913: Answer and Explanation

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Question: 913


The graph of y = f(x) is given above. For what value of x is y = f(x – 4) undefined?

  • A. -3
  • B. 1
  • C. 2
  • D. 5

Correct Answer: D



Difficulty: Easy

Category: Passport to Advanced Math / Functions

Strategic Advice: Algebraically, a function is undefined when a value (or values) in its domain cannot be evaluated (for example, taking the square root of a negative number or dividing by 0). Graphically, this produces a "hole" (or an asymptote) in the graph.

Getting to the Answer: The graph of f(x), which is shown, is undefined at x = 1 because there is a hole in the graph, meaning that the function cannot be evaluated at x = 1. The question asks where the transformed (shifted) function is undefined. The notation y = f(x - 4) represents a horizontal shift of f(x) to the right 4 units (remember, horizontal shifts are always the opposite of how they appear), so imagine moving the hole shown in the graph to the right 4 units. The result is (5, 2), so the shifted function is undefined at x = 5, which is (D).

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