Stretching Functions in MYP Extended Maths

Q: What does Transformation Functions 3 cover?

Builds on earlier transformation work by focusing on combining multiple transformations in the correct order and reverse-engineering equations from transformed graphs. You learn how horizontal shifts, vertical shifts, stretches, and reflections interact when applied together, and how the order changes the final graph. You also practise reading a transformed curve and writing its equation in the form a*f(b(x-h))+k.

Q: Most common mistake with order of transformations?

Students often apply horizontal transformations in the wrong order. Inside-the-bracket changes act opposite to intuition and must be done in reverse: for f(2x-6), factor first to f(2(x-3)), then shift right by 3 and horizontally compress by factor 2. Safe rule: vertical follow standard order (stretch then shift), horizontal are reversed (shift then stretch). When extracting equations from a graph, identify the new vertex first.

Learn vertical and horizontal stretches of functions in MYP Extended Maths Year 5. Master af(x) and f(bx) with clear scale factor rules and worked examples.

Practice

Transformation Functions 3

180 min0 marks

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What Is a Stretch?

A stretch scales a graph — making it taller or flatter, narrower or wider — without moving it to a different location. Stretches are distinct from translations and reflections because they change the distances between points, not just their position or sign. At Extended level, you need to handle both vertical and horizontal stretches with precision.

Vertical Stretch: af(x)

Multiplying the output by a constant a gives y = af(x). This stretches the graph vertically by a scale factor of a:

If a > 1, the graph is stretched away from the x-axis (taller).
If 0 < a < 1, the graph is compressed toward the x-axis (flatter).
If a < 0, there is also a reflection in the x-axis (covered in Transformation Functions 2).

Every point (x, y) becomes (x, ay). The x-intercepts stay fixed; the y-intercept and all other y-values scale by a.

Horizontal Stretch: f(bx)

Replacing x with bx inside the function gives y = f(bx). This stretches the graph horizontally by a scale factor of 1/b:

If b > 1, the graph is compressed horizontally (narrower).
If 0 < b < 1, the graph is stretched horizontally (wider).

Every point (x, y) becomes (x/b, y). The y-intercept is unchanged; the x-intercepts and all other x-values scale by 1/b. As with horizontal translations, the scale factor is the reciprocal of b — a common source of confusion.

Worked Example

Start with f(x) = x². Then 2f(x) = 2x² is a narrower parabola (vertical stretch, scale factor 2). And f(2x) = (2x)² = 4x² — also appears narrower but for a different reason (horizontal compression, scale factor 1/2). Understanding the distinction matters for Criterion C communication tasks.

Common Mistakes

Confusing af(x) and f(bx) — one scales y-values, the other scales x-values.
Forgetting that f(bx) has a horizontal scale factor of 1/b, not b.
Not updating the x-intercepts when applying a horizontal stretch.

Frequently asked questions

Builds on earlier transformation work by focusing on combining multiple transformations in the correct order and reverse-engineering equations from transformed graphs. You learn how horizontal shifts, vertical shifts, stretches, and reflections interact when applied together, and how the order changes the final graph. You also practise reading a transformed curve and writing its equation in the form a*f(b(x-h))+k.

Students often apply horizontal transformations in the wrong order. Inside-the-bracket changes act opposite to intuition and must be done in reverse: for f(2x-6), factor first to f(2(x-3)), then shift right by 3 and horizontally compress by factor 2. Safe rule: vertical follow standard order (stretch then shift), horizontal are reversed (shift then stretch). When extracting equations from a graph, identify the new vertex first.

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