Question

question 19 of 25
what are the domain and range of ( y = \tan x )? select one choice for domain and one for range.
a. range: ( - 1 leq y leq 1 )
b. range: all real numbers
c. domain: all real numbers
d. domain: ( x
eq \frac { pi } { 2 } + n pi )

Explanation:

The tangent function \( y = \tan x \) is defined as \( \frac{\sin x}{\cos x} \). It is undefined when \( \cos x = 0 \), which occurs at \( x = \frac{\pi}{2} + n\pi \) (where \( n \) is any integer). For the range, \( \tan x \) can take any real number value as \( x \) approaches these undefined points (it goes to \( \pm\infty \)) and covers all real numbers in between.

Answer:

B. Range: All real numbers, D. Domain: \( x
eq \frac{\pi}{2} + n\pi \)