Question

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

Answer 1

Answer:

Option C and D that is y= tan x and y= cot x

Step-by-step explanation:

The range is the values of y means the values that y can take in a function:

So, range of tan x and cot x are all real numbers.

Period of  tan x is $\pi$

Period of cot x is $\pi$

Option A and B that is secx and csc x are discarded  

Answer 2

Answer with explanation:

Given a function, y=f(x)

The Set of values that ,x can take for which y is defined is called domain of the function.

And,the set of values that ,y can take for which x ,is defined is called range of function.

For example:→Consider the function, y=x²

→y is defined for all values of x,so Domain is set of real numbers.→(-∞,∞)

→x is defined for positive values of y,so range of this function is [0, ∞).

A:→ y =sec x

Range =(-∞,-1]∪[1,∞)

B: →y=Cosec x

Range =(-∞,-1]∪[1,∞)

C:→y=tan x

Range =(-∞,∞)

D:→y=cot x

Range=(-∞,∞)

→→Option C and D⇒Tan x and Cot x, are trigonometric function ,whose range are set of all Real Numbers.