Functions and graphsUnit 1

Transformations of - words to notation

Apply each instruction to the current graph in the stated order.

  • Keep track of the equation after every transformation.
  • A later horizontal transformation acts on the whole input expression already present.
  • Translations and reflections generally give different results when their order is reversed.

Example 1

Translate by , then reflect in the -axis.

  1. Translate first

    Translate by .

  2. Reflect next

    Replace the current input by .

Original:
Original graph y = f(x).
Image:
Original dashed graph and its transformed solid green image.
Original graphTransformed graph
  • Compare the final turning point with the other example: the two orders give different graphs.

Example 2

Reflect the same graph in the -axis, then translate by .

  1. Reflect first

    Reflect in the -axis.

  2. Translate next

    In the reflected function replace by , then subtract 1.

Original:
Original graph y = f(x).
Image:
Original dashed graph and its transformed solid green image.
Original graphTransformed graph
  • Compare the final turning point with the other example: the two orders give different graphs.

Remember
In these examples, the same starting graph has turning point . The final turning points are and .

Your turn

5 practice questions
Question 1

Translate by , then reflect in the -axis. Write the new equation and map .

Check answer
Original point.After the first transformation.After the second transformation.
Equation Image
Question 2

Reflect in the -axis, then translate by . Write the new equation and map .

Check answer
Original point.After the first transformation.After the second transformation.
Equation Image
Question 3

Translate by , then reflect in the -axis. Write the new equation and map .

Check answer
Original point.After the first transformation.After the second transformation.
Equation Image
Question 4

Reflect in the -axis, then translate by . Write the new equation and map .

Check answer
Original point.After the first transformation.After the second transformation.
Equation Image
Question 5

Translate by , then reflect in the -axis. Write the new equation and map .

Check answer
Original point.After the first transformation.After the second transformation.
Equation Image
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