What is the equation of the graph below? a) y = sec(x) + 2 b) y = csc(x) + 2 c) y = csc(x + 2) d) y = sec(x + 2)

Using a graphing calculator, we can clearly see ther answer is

csc(x) +2

Step-by-step explanation:

We can plot each of those functions you specify and easily demonstrate which graph is the correct one.

Option: B is the correct answer.

The equation of the given graph is:

                      B) y = csc(x) + 2

A)

y=sec(x)+2

We know that when x=0 the graph of this function gives the value as:

y=f(0)=sec 0+2

y=1+2

y=3

But from the given graph we see that the function goes to infinity as x→0.

Hence, option: A is incorrect.

C)

y=csc(x+2)

We know that when x=0 the graph of this function gives the value as:

y=f(0)=csc(0+2)=csc(2)≈1.1

y≈1.1

But from the given graph we see that the function goes to infinity as x→0.

Hence, option: C is incorrect.

D)

y=sec(x+2)

We know that when x=0 the graph of this function gives the value as:

y=f(0)=sec(0+2)=sec(2)≈ -0.2403

y≈ -0.2403

But from the given graph we see that the function goes to infinity as x→0.

Hence, option: D is incorrect.

B)

                                 y =csc(x) + 2

We see that for each value of x the graph of this function matches the graph that is given to us.

          Hence, option: B is correct.

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