Practice Scaling Functions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Scaling a function multiplies its output by a constant (vertical scaling) or compresses/stretches its input (horizontal scaling), changing amplitude or period without changing the shape.

Vertical scaling stretches or squishes the graph up/down; horizontal scaling stretches or squishes it left/right. Both change the function's measurements without altering its fundamental character.

Example 1

easy
Describe how g(x)=3f(x) and h(x)=\frac{1}{2}f(x) transform the graph of f(x)=\sqrt{x}. Evaluate both at x=4.

Example 2

medium
Explain the difference between g(x)=f(2x) (horizontal scaling) and h(x)=2f(x) (vertical scaling) for f(x)=x^2. Compare at x=3.

Example 3

easy
The graph of f has a maximum at (2, 5). Where is the maximum of y=4f(x)? Of y=f(3x)?

Example 4

hard
Starting from f(x)=\sin(x), write the equation and describe each transformation for g(x)=3\sin(2x). State the amplitude and period of g.
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