Scaling Functions Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

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

Solution

  1. 1
    y=4f(x)y=4f(x): vertical scaling multiplies yy-values by 44. Maximum moves from (2,5)(2,5) to (2,20)(2, 20).
  2. 2
    y=f(3x)y=f(3x): horizontal compression divides xx-values by 33. Maximum moves from (2,5)(2,5) to (23,5)(\frac{2}{3}, 5).

Answer

4f(x)4f(x): maximum at (2,20)(2,20); f(3x)f(3x): maximum at (23,5)(\frac{2}{3},5)
Vertical scaling changes yy-coordinates only; horizontal scaling changes xx-coordinates only. For f(bx)f(bx), xx-coordinates are divided by bb (moved closer to the yy-axis when b>1b>1).

About Scaling Functions

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.

Learn more about Scaling Functions →

More Scaling Functions Examples

Example 1 easy

Describe how [formula] and [formula] transform the graph of [formula]. Evaluate both at [formula].

Example 2 medium

Explain the difference between [formula] (horizontal scaling) and [formula] (vertical scaling) for [

Example 4 hard

Starting from [formula], write the equation and describe each transformation for [formula]. State th

← All Scaling Functions Examples Scaling Functions Concept