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Which of the following equations can represent the graph? Select 3 of the following that apply.

Which of the following equations can represent the graph? Select 3 of the following-example-1
Which of the following equations can represent the graph? Select 3 of the following-example-1
Which of the following equations can represent the graph? Select 3 of the following-example-2
User Dynelight
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1 Answer

5 votes

Answer:

The correct options are:


  • y=f(x)=-\sec ((x)/(3))+2

  • y=f(x)=\sec((x)/(3)+\pi)+2

  • y=f(x)=\csc ((x)/(3)+(3\pi)/(2))+2)

Explanation:

a)


y=f(x)=-\sec ((x)/(3))+2

When we plot the graph of this function we see that it matches the given graph.

Hence, option: a is correct.

b)


y=f(x)=\sec ((x)/(3))+2

when x=0 then we hvae:

y=3≠1

( since in the given graph at x=0 the graph is at 1)

Hence, option: b is incorrect.

c)


y=f(x)=-\sec((x)/(3)+\pi)+2

We know that:


\sec(\pi+\theta)=-sec \theta

Hence, we get the above expression as:


y=\sec ((x)/(3))+2 which is same as the expression in option: b

Hence, option: c is incorrect.

d)


y=f(x)=\sec((x)/(3)+\pi)+2

We know that:


\sec(\pi+\theta)=-sec \theta

Hence, we get the above expression as:


y=-\sec ((x)/(3))+2 which is same as the expression in option: a

Hence, option: d is correct.

e)


y=f(x)=-\csc ((x)/(3)+(3\pi)/(2))+2--------(1)

We know that:


\csc ((3\pi)/(2)+\theta)=-\sec \theta

Hence, we get expression (1) as:


y=\sec ((x)/(3))+2 which matches the expression as in option: b.

Hence, option: e is incorrect.

f)


y=f(x)=\csc ((x)/(3)+(3\pi)/(2))+2--------(2)

We know that:


\csc ((3\pi)/(2)+\theta)=-\sec \theta

Hence, we get expression (2) as:


y=-\sec ((x)/(3))+2 which matches the expression as in option: a.

Hence, option: f is correct.

User PercyPham
by
8.0k points

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