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. Which description fits the rule -f(x)?

    • a reflection in the y-axis
    • a reflection in the x-axis
    • a slide down by 1
    • a stretch by a factor of 2

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

    Circle one:   True   False

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

    Answer: ______________

  4. The rule f(x + 2) moves the graph of f in which direction?

    • right by 2
    • up by 2
    • left by 2
    • down by 2

  5. The point (3, 1) lies on the graph of f. Its image under f(x + 2) - 4 is the point (p, q). What is p + q?

    Answer: ______________

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

    Answer: ______________

  7. At the point (2, 1), the rules 3f(x) and 3(f(x) + 2) give the same value of y.

    Circle one:   True   False

  8. The image of the point (5, 4) under the rule f(x + 3) is:

    • (8, 4)
    • (5, 7)
    • (2, 7)
    • (2, 4)

  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. The point (a, b) lies on the graph of f, and its image under f(x - 1) - 3 is (6, -4). What is a + b?

    Answer: ______________

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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. a reflection in the x-axis · The minus sign flips the sign of every output, which turns the graph upside down: a reflection in the x-axis.
  2. 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.
  3. 9 · The rule f(x - 5) slides the graph right by 5, so the x becomes 4 + 5 = 9 and the y stays 3.
  4. left by 2 · The +2 sits inside the brackets, so it acts on the input. The same output now needs an input 2 smaller, so the graph slides left.
  5. -2 · The horizontal move sends x to 3 - 2 = 1, and the vertical move sends y to 1 - 4 = -3. The image is (1, -3), so p + q = 1 + (-3) = -2.
  6. -9 · The rule multiplies every output by -3: -3 times 3 is -9, and the x stays 2.
  7. False · 3f(x) gives 3 times 1 = 3. But 3(f(x) + 2) adds 2 first, then triples: 3 times (1 + 2) = 9. The brackets change the order, so the values differ.
  8. (2, 4) · The rule f(x + 3) slides the graph left by 3, so the x becomes 5 - 3 = 2 and the y stays 4.
  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. 4 · Working back: the horizontal move gives a + 1 = 6, so a = 5. The vertical move gives b - 3 = -4, so b = -1. Then a + b = 5 + (-1) = 4.
Worksheet · LightMySky