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Chapter 6: Q. 71 (page 411)

Find an equation for the graph.

Short Answer

Expert verified

The equation of the given graph is y=-1cos4π3x+1.

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 the minimum is at its y-intercept, then the graph is a cosine function and A<0. Then,

ymin=0ymax=2

02

Step 2. Find the amplitude and period.

Consider the given question,

A=12ymax-yminA=-122-0A=-1

The period is 32. So,

2πω=32ω=4π3

03

Step 3. Form the equation.

Vertical shift,

b=12ymax+yminb=122+0b=122b=1

Consider the form of the function,

y=Acosωx+b

Substitute the values,

y=-1cos4π3x+1

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