Question

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

Answer 1

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.