FunctionsAI HL

Reflections of

Recognise reflections in either coordinate axis.

  • : reflection in the -axis.
  • : reflection in the -axis.
  • Points on the mirror line stay fixed.

Example 1

Reflect in the -axis. Sketch and label the image.

  1. Keep the mirror coordinate

    Reflect in the -axis. Keep the input; reverse the sign of each output.

  2. Write the equation

    The minus sign outside the function gives this reflection.

Original:
Original graph y = f(x).
Image:
Original dashed graph and its transformed solid green image.
Original graphTransformed graphMirror line

Example 2

Reflect in the -axis. Sketch and label the image.

  1. Keep the mirror coordinate

    Reflect in the -axis. Reverse the sign of each input; keep its output.

  2. Write the equation

    The minus sign inside the function gives this reflection.

Original:
Original graph y = g(x).
Image:
Original dashed graph and its transformed solid green image.
Original graphTransformed graphMirror line

Remember
A minus sign inside and a minus sign outside have different effects.

Your turn

5 practice questions
Question 1

Reflect in the -axis. Write the new equation and find the image of .

Check answer
Equation Image
Question 2

Reflect in the -axis. Write the new equation and find the image of .

Check answer
Equation Image
Question 3

Reflect in the -axis. Write the new equation and find the image of .

Check answer
Equation Image
Question 4

Reflect in the -axis. Write the new equation and find the image of .

Check answer
Equation Image
Question 5

Reflect in the -axis. Write the new equation and find the image of .

Check answer
Equation Image
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