Answer:
We are given the tangent function
.
Firstly we know that,
, where
is the sine function and
is the cosine function.
Now, tangent function will be zero when its numerator is zero.
i.e.
when
.
i.e.
when
, where n is the set of integers.
So, tangent function crosses x-axis at
, n is the set of integers.
Further, tangent function will be undefined when its denominator is zero.
i.e.
when
.
i.e.
when
, where n is the set of integers.
Moreover, a zero in the denominator gives vertical asymptotes.
So, tangent function will have vertical asymptotes at
, n is the set of integers.
Therefore, these key features gives us the graph of a tangent function as shown below.