Answer please

Option C.

Step-by-step explanation:

Ok, first we know that:

Tan(0) = 0

While in the graph, we can see that:

f(0) = -2

Then our function will be something like:

f(x) = tan( k*x) - 2

We also can see that the graph has asymptotes at x = π/2 and at x = -π/2

While the normal tangent equation has the asymptotes at x = pi

So here we have that:

k*(pi/2) = pi

k = pi*(2/pi) = 2

k = 2

then the function is something like:

f(x) = tan(2*x) - 2

If we look at the options, we can see one that is:

tan( 2*(x + π)) - 2

we can rewrite this as:

tan(2*x + 2π) - 2

And remember that the period of a trigonometric function is 2π

This means that:

tan(a + 2π) = tan(a)

Then:

tan(2*x + 2π) - 2 =  tan(2*x) - 2

Which is the function that we found.

Then the correct option is C

a

step-by-step explanation: