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What are the domain and range of y = tan X? Select one choice for domain
and one for range.
A. Range: -1 B. Domain: 2 + + na
O C. Domain: All real numbers
O D. Range: All real numbers

What are the domain and range of y tan X Select one choice for domain and one for range A Range 1 B Domain 2 na O C Domain All real numbers O D Range All real n class=

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From photo you would choose B and D.
Your options make no sense.

tan(x) = sin(x) / cos(x) so the domain is restricted by excluding x where cos(x) = 0
This happens when x = pi/2 and repeats every pi after that = pi/2 + n x pi where n is an integer
I don’t like the wording of B but it is the best definition of domain in the question.

The domain of [tex]tanx[/tex] is [tex]R - (n\pi -\frac{\pi }{2})[/tex].

The range of the given function [tex]y = tanx[/tex] is the set of all real numbers.

What is domain?

The domain of a function is the set of values that we are allowed to plug into our function.

What is range?

The range of a function is the set of its possible output values.

According to the given question.

We have a function

[tex]y = tanx[/tex]

The above function can be written as

[tex]y = \frac{sinx}{cosx}[/tex]

⇒ [tex]tanx[/tex] is defined for all values except the values that makes [tex]cosx = 0[/tex], a fraction with denominator is not defined.

And we know that

[tex]cosx = 0 \ \forall \ x \in \frac{(2n+1)\pi }{2} \ where \ n \in Z[/tex]

Hence, for all these values, [tex]tanx[/tex] is not defined.

Therefore, the domain of [tex]tanx[/tex] is [tex]R - (n\pi -\frac{\pi }{2})[/tex].

Since, the domain of  [tex]tanx[/tex] is [tex]R - (n\pi -\frac{\pi }{2})[/tex], so when we input these values in the given function we get only real numbers.

Therefore, the range of the given function [tex]y = tanx[/tex] is the set of all real numbers.

Thus, option D and B are correct.

Find out more information about domain and range here:

https://brainly.com/question/1632425

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