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Chapter 6: Q. 40 (page 435)

In Problems 39 and 40 , find a function whose graph is given.

Short Answer

Expert verified

The function isy=-7sinπ4x

Step by step solution

01

Given information

Given graph

02

Identify the amplitude

From the graph that it has an amplitude of 7. We can also see that it starts from (0,0), therefore, we can say that it is a sine function. We can also see that instead of the normal sine that it goes up, it goes down which means that it is a negative sine function. A sine function takes the form y=Asin(ωx-ϕ)+B. We can see that the period of cosine is 8 therefore we are going to use the formula T=2πω

T=2πω8=2πωω=π4

03

Checking the phase shift and forming the function

We can safely assume that ϕand Bis 0 since there is no phase shift in the graph and there are no vertical translations. Listing the values that we have and B=0. The function of the graph is

y=-7sinπ4x

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