Answer:
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
