Question

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. y=sec x
B. y= tan x
C. y= cot x
D. y= csc x

Answer 1

I believe it is A and D

Answer 2

A. y=sec x

D. y= csc x

Explanation:

We have that,

Range of the functions is the set of all real numbers greater than or equal to 1 or less than or equal to -1.

As, we know that,

Range of the functions, y = tanx and y = cotx is
`(-\infty,\infty)` i.e. the set of all real numbers.

So, options B and C are discarded.

Since,
`\csc x=(1)/(\sin x)` and
`\sec x=(1)/(\cos x)`.

Thus, their range will be greater than the the range of y = sinx and y = cosx.

Now, as it is known that the range of the functions y = sinx and y = cosx is [-1,1].

Then, the range of y=sec x and y= csc x is the set of all real numbers greater than or equal to 1 or less than or equal to -1.

Hence, options A and D are correct.