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Chapter 6: Q. 73 (page 411)

Find an equation for the graph.

Short Answer

Expert verified

The equation of the given graph is y=3sinπ2x.

Step by step solution

01

Step 1. Determine the sinusoidal function.

Consider the given graph,

The type of sinusoidal graph can be determined immediately by inspecting its y-intercept if its at a maximum(highest point) and a minimum(lowest point) or neither.

As there is neither a maximum or minimum at its y-intercept, then the graph is a sine function and the minimum occurs before the maximum and A>0. Then,

ymax=3ymin=-3

02

Step 2. Find the amplitude and period.

Consider the given question,

A=12ymax-yminA=123--3A=126A=3

The period is 4. So,

2πω=4ω=2π4ω=π2

03

Step 3. Form the equation.

Vertical shift,

b=12ymax+yminb=123-3b=0

Consider the form of the function,

y=Asinωx+b

Substitute the values,

y=3sinπ2x+0y=3sinπ2x

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