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Math lesson plan · 11th grade (Year 12 in England) · 45 minutes

Describe the transformation from y = f(x)

Algebra

CCSS HSF.BF.B.3England: A-level Pure Mathematics

Objective and success criteria

Students will: Describe the transformation from y = f(x).

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Transformations of functions

Leads to: the next skill in this area.

Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Transformations of functions). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Which transformation maps y = f(x) to y = f(x) + 5? (translate up 5 / translate left 5 / reflect in the x-axis / reflect in the y-axis) → translate up 5Prompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).
  2. Which transformation maps y = f(x) to y = f(x + 4)? (translate up 4 / translate left 4 / reflect in the x-axis / reflect in the y-axis) → translate left 4Prompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).
  3. Which transformation maps y = f(x) to y = f(x + 2)? (translate up 2 / translate left 2 / reflect in the x-axis / reflect in the y-axis) → translate left 2Prompt: Changes outside f affect y; changes inside f affect x (and act the opposite way).

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Describe the transformation from y = f(x). Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: Which transformation maps y = f(x) onto y = −f(x)?
  • Step 1: Reflection in the x-axis
  • Answer: Reflection in the x-axis
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. Which transformation maps y = f(x) onto y = f(−x)? (Reflection in the x-axis / Reflection in the y-axis / Horizontal stretch, scale factor 5 / Horizontal stretch, scale factor 1/5) → Reflection in the y-axisPrompt: Changes outside the bracket act vertically; inside act horizontally.
  2. The point (2, 2) lies on y = f(x). Where does it move to on y = 5f(x)? Type it like (2, −1). → (2, 10)Prompt: Outside changes affect the y-coordinate.

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. The point (0, −3) lies on y = f(x). Where does it move to on y = f(x − 2) − 4? Type it like (2, −1). → (2, −7)Prompt: Outside changes affect the y-coordinate.
  2. Which transformation maps y = f(x) onto y = −f(x)? (Horizontal stretch, scale factor 4 / Translation 4 units right / Reflection in the x-axis / Vertical stretch, scale factor 4) → Reflection in the x-axisPrompt: Changes outside the bracket act vertically; inside act horizontally.

Watch out for

  • Doing an operation to one side of an equation but not the other.
  • Reading 3x as 3 + x, or thinking x always stands for one particular number.

Support and stretch

Support

  • Review first: Transformations of functions.
  • Use concrete materials: balance scales or a balance drawing.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.

Free lesson plan from eurekami.com/lesson-plan-builder

eurekami

Describe the transformation from y = f(x)

Name

Date

Score/ 8

  1. Question 1

    Which transformation maps y = f(x) onto y = f(x) + 3?

    • A. Translation 3 units up
    • B. Vertical stretch, scale factor 3
    • C. Reflection in the y-axis
    • D. Reflection in the x-axis

  2. Question 2

    The point (−5, −6) lies on y = f(x). Where does it move to on y = −f(x)? Type it like (2, −1).

    Answer

  3. Question 3

    The point (2, 5) lies on y = f(x). Where does it move to on y = 2f(x)? Type it like (2, −1).

    Answer

  4. Question 4

    Which transformation maps y = f(x) onto y = 5f(x)?

    • A. Horizontal stretch, scale factor 1/5
    • B. Reflection in the y-axis
    • C. Translation 5 units left
    • D. Vertical stretch, scale factor 5

  5. Question 5

    The point (1, 2) lies on y = f(x). Where does it move to on y = f(x + 4) − 4? Type it like (2, −1).

    Answer

  6. Question 6

    Which transformation maps y = f(x) onto y = f(2x)?

    • A. Translation 2 units up
    • B. Reflection in the y-axis
    • C. Horizontal stretch, scale factor 1/2
    • D. Horizontal stretch, scale factor 2

  7. Question 7

    The point (−5, 4) lies on y = f(x). Where does it move to on y = −f(x)? Type it like (2, −1).

    Answer

  8. Question 8

    Which transformation maps y = f(x) onto y = f(x) + 5?

    • A. Horizontal stretch, scale factor 1/5
    • B. Translation 5 units left
    • C. Translation 5 units up
    • D. Horizontal stretch, scale factor 5

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Answer key: Describe the transformation from y = f(x)

  1. 1. A. Translation 3 units up

  2. 2. (−5, 6)

  3. 3. (2, 10)

  4. 4. D. Vertical stretch, scale factor 5

  5. 5. (−3, −2)

  6. 6. C. Horizontal stretch, scale factor 1/2

  7. 7. (−5, −4)

  8. 8. C. Translation 5 units up