Q:

Which of the functions have a range of all real numbers? Check all that apply. A. y = sec x B. y = tan x C. y = cot x D. y = csc x

Accepted Solution

A:
Answer:B. y = tan x  and  C. y = cot xStep-by-step explanation:Range:range is defined as the set of values that any given function y=f(x), can take for which the x values are defined. It is the value that y can take for the values of x.Given:From the given optionsthe range of tanx and cotx are all real numbersas the period of tanx and cotx are πwhere as range of secx is all real numbers except π/2 + n*π i.e. (-∞ , -1] U [1 , + ∞)And range of cscx is all real numbers except n*π i.e.(-∞ , -1] U [1 , + ∞)So from the given option:option B and C are correct while A and D are not !