Function Transformations • Topic 3 of 4

Stretching

Multiplying a function by a constant greater than 1 stretches its graph vertically: a·f(x) with a > 1 makes every output a times larger, pulling the graph away from the x-axis so it looks taller and narrower. For example, y = 3x² is a vertical stretch of y = x² by a factor of 3 — at each x its height is tripled. The x-intercepts stay put (multiplying 0 by a is still 0), but other points rise. A vertical stretch is the opposite of a compression, which uses a factor between 0 and 1. The SAT tests identifying a vertical stretch and its factor from an equation like a·f(x).

sat33t3 graphOVertical stretchy = 3x²: stretched vertically (narrower)y = x² (parent)transformed

✅ Solved examples

1. y = x² becomes y = 4(x²). What transformation is this?
A vertical stretch by a factor of 4.
2. y = |x| becomes y = 3|x|. What transformation?
A vertical stretch by a factor of 3.
3. Does multiplying a function by 5 stretch or compress it?
Stretch (factor > 1).
4. y = x³ becomes y = 2x³. Transformation?
A vertical stretch by a factor of 2.

✏️ Practice — try these, take hints as needed

1. y = x² becomes y = 6(x²). What transformation?
Factor > 1.
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A vertical stretch by a factor of 6.
2. y = |x| becomes y = 5|x|. What transformation?
Factor 5 > 1.
—
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A vertical stretch by a factor of 5.
3. Multiplying a function by 8 produces a vertical:
> 1 → ?
—
—
Stretch.
4. y = √x becomes y = 7√x. What transformation?
Factor 7.
—
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A vertical stretch by a factor of 7.
5. A vertical stretch makes a graph look taller and:
Pulled away from x-axis.
—
—
Narrower.

📝 Topic test — 8 questions

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