Mathematics Advanced Year 11 - Module 1 - Lesson 10

Reflections of Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

When a video game character turns around, the artist does not redraw the entire sprite — they simply flip the image horizontally. In mathematics, we can flip graphs too: across the $x$-axis, across the $y$-axis, or both. These reflections are powerful tools for sketching and understanding symmetry.

  • $-f(x)$ reflects the graph in the $x$-axis
  • How reflections affect the coordinates of key points

2. Success Criteria

By the end, you should be able to:

  • $-f(x)$ reflects the graph in the $x$-axis
  • $f(-x)$ reflects the graph in the $y$-axis
  • $-f(-x)$ reflects in both axes

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "$-f(x)$ reflects the graph in the $x$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "$f(-x)$ reflects the graph in the $y$-axis". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Reflections of Functions: "$-f(-x)$ reflects in both axes".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Reflections of Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Reflections of Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Reflections of Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: $-f(x)$ reflects the graph in the $x$-axis

Band 32 marks
Success criterion 2

Prove that you can: $f(-x)$ reflects the graph in the $y$-axis

Band 43 marks
Success criterion 3

Prove that you can: $-f(-x)$ reflects in both axes

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 10

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Mathematics Advanced Year 11 - Module 1 - Lesson 10

Reflections of Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

When a video game character turns around, the artist does not redraw the entire sprite — they simply flip the image horizontally. In mathematics, we can flip graphs too: across the $x$-axis, across the $y$-axis, or both. These reflections are powerful tools for sketching and understanding symmetry.

  • $-f(x)$ reflects the graph in the $x$-axis
  • How reflections affect the coordinates of key points

2. Success Criteria

By the end, you should be able to:

  • $-f(x)$ reflects the graph in the $x$-axis
  • $f(-x)$ reflects the graph in the $y$-axis
  • $-f(-x)$ reflects in both axes

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "$-f(x)$ reflects the graph in the $x$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "$f(-x)$ reflects the graph in the $y$-axis". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Reflections of Functions: "$-f(-x)$ reflects in both axes".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Reflections of Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Reflections of Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Reflections of Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: $-f(x)$ reflects the graph in the $x$-axis

Band 32 marks
Success criterion 2

Prove that you can: $f(-x)$ reflects the graph in the $y$-axis

Band 43 marks
Success criterion 3

Prove that you can: $-f(-x)$ reflects in both axes

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 10

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Mathematics Advanced Year 11 - Module 1 - Lesson 10

Reflections of Functions

Use this worksheet after reading the lesson to practise the key ideas and prove you can meet the success criteria.

Name
Date
Class

1. Key Ideas

When a video game character turns around, the artist does not redraw the entire sprite — they simply flip the image horizontally. In mathematics, we can flip graphs too: across the $x$-axis, across the $y$-axis, or both. These reflections are powerful tools for sketching and understanding symmetry.

  • $-f(x)$ reflects the graph in the $x$-axis
  • How reflections affect the coordinates of key points

2. Success Criteria

By the end, you should be able to:

  • $-f(x)$ reflects the graph in the $x$-axis
  • $f(-x)$ reflects the graph in the $y$-axis
  • $-f(-x)$ reflects in both axes

3. Key Terms

FunctionA relation where each input has exactly one output.
DomainThe set of all possible input values for a function.
RangeThe set of all possible output values for a function.
Inverse FunctionA function that reverses the effect of the original function.
QuadraticA polynomial of degree 2, in the form ax² + bx + c.
DiscriminantThe expression b² - 4ac that determines the nature of quadratic roots.

4. Activity: Build the Lesson Map

Use the lesson to complete the table. Keep answers brief but specific.

PromptYour answer
Main concept
Important example
Common mistake to avoid
How this links to the next lesson

5. Short Answer Questions

1. Explain this lesson goal in your own words: "$-f(x)$ reflects the graph in the $x$-axis". Use one specific example from the lesson.

Band 32 marks

2. Apply this idea to a new example: "$f(-x)$ reflects the graph in the $y$-axis". Show your reasoning clearly.

Band 43 marks

3. Analyse why this idea matters for understanding Reflections of Functions: "$-f(-x)$ reflects in both axes".

Band 54 marks

6. Extend: Apply the Idea

Band 5/65 marks

A student gives a memorised answer about Reflections of Functions but does not use evidence or reasoning.

Improve the answer by writing a stronger response that uses accurate terminology, a relevant example and a clear explanation.

7. Multiple Choice

1. What is the best first step when answering a question about Reflections of Functions?

A. Identify the key concept being tested

B. Write every fact from memory

C. Ignore the command word

D. Skip examples and evidence

2. Which answer would show stronger understanding of Reflections of Functions?

A. An answer with accurate terms and reasoning

B. A copied definition only

C. A single-word response

D. An answer with no example

3. What should you do if a question asks you to explain?

A. Link the idea to a reason or cause

B. List unrelated facts

C. Only draw a diagram

D. Write the shortest possible answer

8. Success Criteria Proof

Finish with evidence that you can do each success criterion.

Success criterion 1

Prove that you can: $-f(x)$ reflects the graph in the $x$-axis

Band 32 marks
Success criterion 2

Prove that you can: $f(-x)$ reflects the graph in the $y$-axis

Band 43 marks
Success criterion 3

Prove that you can: $-f(-x)$ reflects in both axes

Band 54 marks

One thing I still need help with:

HSCScience - Printable lesson worksheet - Mathematics Advanced Year 11 - Module 1 - Lesson 10