Lesson 2 of 3
Use the reciprocal horizontal factor and direct vertical factor.
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Worked example · 1 of 8
Worked example
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If , find . Check: the input remains 2 and the new output is 12.
Big ideas
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For , output v becomes . A vertical stretch has ; a vertical compression has . Negative a also reflects across the x-axis.
For , with b nonzero, input u becomes . A horizontal compression has ; a horizontal stretch has .
A negative inside factor b also reflects across the y-axis. The horizontal distance factor is , not |b|.
For , a known point becomes . Check it by substitution. Scale the domain horizontally and the range vertically.
Worked example
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Map to . Solve for , and compute . The image shows horizontal compression and reflected vertical compression.
Step-through
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A point (6,-4) lies on f. Find its corresponding point on g(x)=-().
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Worked example
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Suppose . For , solve , giving . Thus . Horizontal distances multiply by 4, even though the inside factor is .
Worked example
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Suppose f has domain and range . For , require , giving domain . Doubling outputs gives range . The negative inside factor reflects input locations, not outputs.
Mix-up alert
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Wrong idea: makes a graph five times wider. Repair: a known input u is reached when , so . The graph compresses horizontally by factor .
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The factor is outside.
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What does 4f(x) do to output coordinates?
Multiplies them by 4.
What happens to input u in f(4x)?
It becomes .
Is a horizontal stretch or compression?
A stretch by factor 3.
What does -2f(x) do?
Reflects across the x-axis and stretches vertically by 2.
What does f(-2x) do?
Reflects across the y-axis and compresses horizontally by .
Map (8,6) under g(x)=f(2x)/3.
(4,2).
What vertical factor compresses to one quarter of each output?
.
Why exclude in a horizontal scale rule?
Dividing by b would be undefined; f(0x) is constant where f(0) exists.
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Self-test
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