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Chapter 6: Q. 72 (page 411)

Find an equation for the graph.

Short Answer

Expert verified

The equation of the given graph is y=-12sin32x-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 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,

ymin=-32ymax=-12

02

Step 2. Find the amplitude and period.

Consider the given question,

A=12ymax-yminA=-12-12--32A=-1222A=-12

The period is 43π. So,

4π3=2πωω=2π4π×3ω=32

03

Step 3. Form the equation.

Vertical shift,

b=12ymax+yminb=12-12+-32b=12-42b=-1

Consider the form of the function,

y=Asinωx+b

Substitute the values,

y=-12sin32x-1

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