FunctionsAI HL

Translations of

Connect a translation vector, function notation and the graph.

  • The graph of is the image under translation by .
  • Adding inside the function moves the graph left; adding outside moves it up.

Example 1

Translate by . Write the equation and sketch the image.

  1. Read the vector

    Move every point 3 right and 2 up.

  2. Write the equation

    Horizontal movement changes the input; vertical movement changes the output.

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

Example 2

Translate by . Write the equation and sketch the image.

  1. Read the vector

    Move every point 2 left and 1 down.

  2. Write the equation

    Horizontal movement changes the input; vertical movement changes the output.

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

Remember
Track a labelled point to check the direction.

Your turn

5 practice questions
Question 1

Translate by . Write the new equation and find the image of .

Check answer
Equation Image
Question 2

Translate by . Write the new equation and find the image of .

Check answer
Equation Image
Question 3

Translate by . Write the new equation and find the image of .

Check answer
Equation Image
Question 4

Translate by . Write the new equation and find the image of .

Check answer
Equation Image
Question 5

Translate by . Write the new equation and find the image of .

Check answer
Equation Image
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