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Math: Functions Flashcards

7 cards from real ACT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. If f(x) = x^2 - 4x + 3, what are the x-intercepts?

    Answer: x = 1 and x = 3

    Factoring gives (x - 1)(x - 3) = 0, so x = 1 and x = 3.

  2. What is the vertex of f(x) = (x - 2)^2 + 5?

    Answer: (2, 5)

    In vertex form, the vertex is (h, k) = (2, 5).

  3. If f(x) = 4x - 1, what is the inverse function f^-1(x)?

    Answer: (x + 1)/4

    Solving y = 4x - 1 for x gives x = (y + 1)/4.

  4. A function f is defined by f(x) = 6/x. What is f(f(3))?

    Answer: 3

    f(3) = 2, then f(2) = 6/2 = 3.

  5. If f(x) = x^3, which statement is true?

    Answer: f is an odd function

    f(-x) = -f(x), which defines an odd function.

  6. What is f(2) for the piecewise function f(x) = x + 1 if x = 2?

    Answer: 4

    Since 2 >= 2, use f(x) = 2x, giving 2(2) = 4.

  7. The graph of f(x) = x^2 is shifted right 3 units. What is the new function?

    Answer: (x - 3)^2

    A rightward shift replaces x with (x - 3).