Scaling Functions Math Example 4

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

Example 4

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

Solution

  1. 1
    Amplitude: coefficient 33 gives vertical stretch โ†’ amplitude =3=3 (max value is 33, min is โˆ’3-3).
  2. 2
    Period: argument 2x2x gives horizontal compression by 12\frac{1}{2} โ†’ period =2ฯ€2=ฯ€= \frac{2\pi}{2}=\pi.
  3. 3
    So g(x)=3sinโก(2x)g(x)=3\sin(2x) oscillates between โˆ’3-3 and 33 with period ฯ€\pi, completing two full cycles on [0,2ฯ€][0,2\pi].

Answer

Amplitude =3=3; Period =ฯ€=\pi
For y=asinโก(bx)y=a\sin(bx), amplitude =โˆฃaโˆฃ=|a| and period =2ฯ€/b=2\pi/b. Vertical scaling controls height (amplitude); horizontal scaling controls width (period). These are independent transformations.

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 โ†’

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 3 easy

The graph of [formula] has a maximum at [formula]. Where is the maximum of [formula]? Of [formula]?

โ† All Scaling Functions Examples Scaling Functions Concept