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Chapter 6: Q. 68 (page 410)

Find an equation for each graph.

Short Answer

Expert verified

Equation for the graph is:

y=-52cosπx

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

Since the minimum is at its y-intercept, then the graph is a cosine function and hence,

A<0

02

Step 2. Find the amplitude and period

From the graph. ymin=-54ymax=54

A=12(ymax-ymin)A=12(54-(-54))A=12(104)A=54

Using the maximum at x=0, the next maximum occurs atx=2

Therefore,

T=2

03

Step 3. Solve for the equation

ω=2π2ω=2π2ω=π

Therefore, the equation of the graph is

y=-52cosπx

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