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

ii),iv and vi

Step-by-step explanation:

Given is a graph which has 3 pieces and we have to find out the equation of the graph from the given options

i) OPtion a)

This graph will be y(0) = sec0+2 =3

But y intercept is not 3.  Hence incorrect

ii)

When x=0 we have y intercept = -3+2 =-1 matches with graph

Also x intercepts when sec x/3 =2

Or when x = multiples of pi(since sec pi/3 =2 )

So ii is correct

iii)

This graph is the transformation of the parent graph by shifting horizontally pi units to left

y(0) = -secpi+2 =1 .

When x =pi, y = -(-2)+2 is not zero. So x intercepts do not match.  Incorrect

iv)

this matches with y intercept as 1, and x intercepts as -pi and pi

Hence correct

v)

This is incorrect since x intercepts 2pi and -2pi do not match with the given graph

vi)

This has x intercepts as pi and -pi and also y intercept as 1.

Hence correct

The correct options are:

a)

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

Hence, option: a is correct.

b)

       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)

We know that:

Hence, we get the above expression as:

  which is same as the expression in option: b

Hence, option: c is incorrect.

d)

We know that:

Hence, we get the above expression as:

  which is same as the expression in option: a

Hence, option: d is correct.

e)

We know that:

Hence, we get expression (1) as:

  which matches the expression as in option: b.

Hence, option: e is incorrect.

f)

We know that:

Hence, we get expression (2) as:

  which matches the expression as in option: a.

Hence, option: f is correct.