Functions and graphsUnit 1

Stretches of

State the direction, scale factor and invariant line.

  • with : stretch parallel to the -axis, scale factor ; invariant line .
  • with : stretch parallel to the -axis, scale factor ; invariant line .
  • A scale factor between 0 and 1 compresses the graph towards the invariant line.

Example 1

Sketch from . State the scale factor and invariant line.

  1. Identify the scale factor

    Stretch parallel to the -axis with scale factor . Distances from the invariant line are multiplied by this factor.

  2. Identify the invariant line

    The -axis stays fixed.

  3. Map the points

    Only heights change.

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

Example 2

Sketch from . State the scale factor and invariant line.

  1. Identify the scale factor

    Stretch parallel to the -axis with scale factor . Distances from the invariant line are multiplied by this factor.

  2. Identify the invariant line

    The -axis stays fixed.

  3. Map the points

    Only horizontal coordinates change.

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

Remember
The horizontal scale factor is the reciprocal of the multiplier of the input.

Your turn

5 practice questions
Question 1

Stretch parallel to the -axis with scale factor . State the invariant line, write the new equation and map .

Check answer
Equation Image

Invariant line .

Question 2

Stretch parallel to the -axis with scale factor . State the invariant line, write the new equation and map .

Check answer
Equation Image

Invariant line .

Question 3

Stretch parallel to the -axis with scale factor . State the invariant line, write the new equation and map .

Check answer
Equation Image

Invariant line .

Question 4

Stretch parallel to the -axis with scale factor . State the invariant line, write the new equation and map .

Check answer
Equation Image

Invariant line .

Question 5

Stretch parallel to the -axis with scale factor . State the invariant line, write the new equation and map .

Check answer
Equation Image

Invariant line .

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