Question

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

Answer 1

Hello!

The answer is: The correct options are B. Tan(x) and C. Cot(x)

Why?

The range is the output of a function when we evaluate the function with inputs (domain), not all functions have a range of all real numbers, however it's more common to find functions without range or domain restrictions.

Both options B. Tan(x) and C. Cot(x) have a range of all real numbers while the functions Sec(x) and Csc (x) have a restricted range.

Sec(x) and Csc(x):

Domain, all real numbers.

Range, from -1 to 1 or [-1,1]

Tan(x) and Cot(x):

Domain, all real numbers except
`(\pi )/(2)+-n\pi`

Range, all real numbers.

Hence, the correct options are B. Tan(x) and C. Cot(x)

Have a nice day!

Answer 2

B. y = tan x and C. y = cot x

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 options

the range of tanx and cotx are all real numbers

as the period of tanx and cotx are π

where 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 !