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Math 30-1 · Worksheets

Transformations · Set B

Ten questions of mixed difficulty, covering Transformations. Print it, or work through it on screen — the answer key starts on its own page.

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Transformations · Set B

Math 30-1 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. The point (3, 4) is on y = f(x). Which point is on y = f(−x)?

    1. a) (−3, 4)
    2. b) (4, 3)
    3. c) (−3, −4)
    4. d) (3, −4)

  2. Compared with y = f(x), the graph of y = f(2x) has:

    1. a) a vertical stretch by a factor of 1/2
    2. b) a horizontal stretch by a factor of 1/2
    3. c) a vertical stretch by a factor of 2
    4. d) a horizontal stretch by a factor of 2

  3. Compared with y = f(x), the graph of y = f(x) + 5 is:

    1. a) translated 5 units left
    2. b) translated 5 units right
    3. c) translated 5 units down
    4. d) translated 5 units up

  4. If f(x) = 2x and g(x) = x + 3, what is (f + g)(x)?

    1. a) 2x² + 6x
    2. b) 3x
    3. c) 3x + 3
    4. d) 2x + 3

  5. If f(x) = x² and g(x) = x + 3, what is g(f(x))?

    1. a) x² + 3
    2. b) x² + x + 3
    3. c) (x + 3)²
    4. d) x³ + 3x²

  6. y = f(x) has domain −2 ≤ x ≤ 6. What is the domain of y = f(2x)?

    1. a) −4 ≤ x ≤ 12
    2. b) 0 ≤ x ≤ 8
    3. c) −1 ≤ x ≤ 3
    4. d) −2 ≤ x ≤ 6

  7. The point (6, 3) is on y = f(x). Which point is on y = −2f(½(x + 4))?

    1. a) (8, −6)
    2. b) (−1, −6)
    3. c) (16, −6)
    4. d) (8, 6)

  8. The graph of the inverse of a function is a reflection of the original graph in:

    1. a) the x-axis
    2. b) the line y = x
    3. c) the line y = −x
    4. d) the y-axis

  9. The graph of y = f(x) is translated 3 units to the right. What is the new equation?

    1. a) y = f(x − 3)
    2. b) y = f(x) + 3
    3. c) y = f(x) − 3
    4. d) y = f(x + 3)

  10. The point (4, −6) is on y = f(x). Which point is on y = 3f(x − 1) + 2?

    1. a) (5, −12)
    2. b) (3, −16)
    3. c) (5, −16)
    4. d) (13, −16)

Answer key · Transformations · Set B

Math 30-1 · maddyhelps.com

  1. a) (−3, 4) — The negative is inside with x, so only x changes sign: a reflection in the y-axis. (3, −4) would be y = −f(x).
  2. b) a horizontal stretch by a factor of 1/2 — A number multiplying x stretches horizontally by its reciprocal, so 2x squeezes the graph toward the y-axis by a factor of 1/2.
  3. d) translated 5 units up — Adding outside the function adds to every y-value, so the whole graph moves up 5. Vertical shifts go the same way as the sign.
  4. c) 3x + 3 — (f + g)(x) just means f(x) + g(x): 2x + x + 3 = 3x + 3. Multiplying them would give 2x² + 6x.
  5. a) x² + 3 — f goes in first: g(x²) = x² + 3. (x + 3)² is the other order, f(g(x)) — composition is not usually the same both ways.
  6. c) −1 ≤ x ≤ 3 — f(2x) compresses horizontally by 1/2, so every x-value is halved: −2 becomes −1 and 6 becomes 3. Doubling them is the common reversal.
  7. a) (8, −6) — x: the ½ stretches horizontally by 2, then shift left 4 — 6 × 2 − 4 = 8. y: stretch by 2 and reflect — 3 × (−2) = −6. Stretches come before translations.
  8. b) the line y = x — An inverse swaps every x and y, and swapping coordinates is exactly a reflection in the line y = x.
  9. a) y = f(x − 3) — Horizontal shifts act on x and go the opposite way to the sign: x − 3 moves the graph right. Adding 3 outside the function would move it up.
  10. c) (5, −16) — x: shift right 1, so 4 + 1 = 5. y: stretch first, then shift — 3 × (−6) + 2 = −16. Shifting before stretching gives the wrong −12.