Transformations of Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Transformations of Graphs

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. The point (4, 3) lies on the graph of f. What is the x-coordinate of its image under f(x - 5)?

    Answer: ______________

  2. Let g(x) = f(x) + 6 and h(x) = f(x) - 3. At any allowed input, what is g(x) - h(x)?

    Answer: ______________

  3. The rule -f(x) reflects the graph of f in the line y = x.

    Circle one:   True   False

  4. The point (-4, 0) lies on the graph of f. Which point is its image under 3f(x)?

    • (-12, 0)
    • (-4, 0)
    • (-4, 3)
    • (-4, -3)

  5. The only transformation is g(x) = Af(x). A tracked point (3, 8) becomes (3, 2). Which rule fits?

    • g(x) = 4f(x)
    • g(x) = -0.25f(x)
    • g(x) = 0.25f(x)
    • g(x) = f(x) - 6

  6. The point (1, 3) lies on the graph of f. What is the y-coordinate of its image under 3f(x) + 2?

    Answer: ______________

  7. Which description separates the scaling and reflection in g(x) = -0.5f(x)?

    • Vertical scale factor 0.5; reflect in the x-axis.
    • Vertical scale factor 2; reflect in the x-axis.
    • Horizontal scale factor 0.5; reflect in the y-axis.
    • Horizontal scale factor 2; reflect in the y-axis.

  8. The point (2, 3) lies on the graph of f. What is the y-coordinate of its image under -3f(x)?

    Answer: ______________

  9. The point (5, -4) lies on the graph of f. Its image under 2f(x - 2) - 1 is the point (p, q). What is p times q?

    Answer: ______________

  10. Tom rewrites 2f(x) + 4 as 2(f(x) + 4). Is his rewrite correct?

    • Yes, because the 2 multiplies everything
    • Yes, the brackets change nothing
    • No, it should be 2f(x) - 4
    • No, 2(f(x) + 4) is 2f(x) + 8
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Transformations of Graphs W1-mt_691_c-7Z5M-s1

  1. 9 · The rule f(x - 5) slides the graph right by 5, so the x becomes 4 + 5 = 9 and the y stays 3.
  2. 9 · Subtract the corresponding outputs: f(x) + 6 - (f(x) - 3) = 6 + 3 = 9.
  3. False · The -f(x) flips every output's sign, which is a reflection in the x-axis. A reflection in the line y = x would swap the coordinates, which is what an inverse does.
  4. (-4, 0) · The x-coordinate stays -4. Multiplying the output 0 by 3 still gives 0, so the point stays at (-4, 0).
  5. g(x) = 0.25f(x) · The image output satisfies 8A = 2, so A = 2/8 = 0.25. A translation by -6 is excluded by the stated form.
  6. 11 · The rule multiplies every output by 3, then adds 2: 3 times 3 is 9, plus 2 is 11. The x stays 1.
  7. Vertical scale factor 0.5; reflect in the x-axis. · The multiplier's magnitude is 0.5, so vertical distances halve. Its negative sign also reflects the graph in the x-axis.
  8. -9 · The rule multiplies every output by -3: -3 times 3 is -9, and the x stays 2.
  9. -63 · The horizontal move sends x to 5 + 2 = 7, and the vertical move sends y to 2*(-4) - 1 = -9. The image is (7, -9), so p times q is 7 * (-9) = -63.
  10. No, 2(f(x) + 4) is 2f(x) + 8 · Expanding 2(f(x) + 4) gives 2f(x) + 8, not 2f(x) + 4. Tom's version would add 8 to every output, not 4.
Worksheet · LightMySky