Using complete sentences, explain the key features of the graph of the tangent function.

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.

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