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

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. A graph has a turning point at (2, 7). What is the y-coordinate of the turning point on the graph of f(x) - 10?

    Answer: ______________

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

    Circle one:   True   False

  4. Which way does the graph of y = f(x) move to make y = f(x + 3)?

    • Left 3
    • Right 3
    • Up 3
    • Down 3

  5. The graph of f(x) has a turning point at (1, 4). What is the turning point of 2f(x)?

    • (1, 8)
    • (2, 4)
    • (1, 2)
    • (1, 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. The graph of f(x) has a turning point at (-3, 5). What is the turning point of -f(x)?

    • (-3, -5)
    • (3, 5)
    • (-3, 5)
    • (3, -5)

  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. -3 · Subtracting 10 outside the brackets moves the whole graph down 10, so the y-coordinate drops by 10.
  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. Left 3 · Adding 3 inside the brackets moves every point 3 spaces to the left, not the right.
  5. (1, 8) · Multiplying f(x) by 2 stretches the graph vertically, doubling every y-value while x stays the same.
  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. (-3, -5) · The negative sign flips the graph over the x-axis, so the y-coordinate becomes its opposite while x stays put.
  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