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Chapter 6: Q. 67 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=34sin2蟺虫

Step by step solution

01

Step 1. Inspecting the y-intercept

Referring to the given graph the type of sinusoid can be determined immediately by inspecting its y- intercept if its at a maximum(highest point) and a minimum(lowest point) or neither

At its y-intercept neither maximum or nor minimum, then the graph is a sine function and hence,A>0

02

Step 2. Find the amplitude and period

From the graph, ymin=-34ymax=34

A=12(ymax-ymin)A=12(34-(-34))A=12(64)A=34

Using the maximum at x=14, the next maximum occurs atx=54

Therefore,

T=1

03

Step 3. Solve for the equation

蝇=2蟺1蝇=2蟺1蝇=2蟺

Therefore, the equation of the graph is

y=34sin2蟺虫

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