SOLUTION: Which of the following functions has domain (-infinity, plus infinity) and range (-1,1)? One of the following is the correct answer. Which one is correct? A) f(x)=sinx B) f(x)=a

Algebra ->  Functions -> SOLUTION: Which of the following functions has domain (-infinity, plus infinity) and range (-1,1)? One of the following is the correct answer. Which one is correct? A) f(x)=sinx B) f(x)=a      Log On


   

Question 1199096: Which of the following functions has domain (-infinity, plus infinity) and range (-1,1)?
One of the following is the correct answer. Which one is correct?
A) f(x)=sinx
B) f(x)=arcsinx
C) f(x)=tanx
D) f(x)=arctanx
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A) f%28x%29=sin%28x%29
domain:
R (all real numbers)
or (-infinity, infinity)
range:
{ f+element R : -1%3C=f%3C=1 }
[-1,1]

B) f%28x%29=arcsin%28x%29
Domain:
{ -1%3C=x%3C=1 }
or
[-1,1]
Range:
{ f+element R : -pi%2F2%3C=f%3C=pi%2F2 }
[-pi%2F2, pi%2F2]


C) f%28x%29=tan%28x%29
Domain:
{ x element R : x%2Fpi+%2B+1%2F2 not element +Z }
Range:
R+(all real numbers)
or
(-infinity, infinity)

D) f%28x%29=arctan%28x%29
Domain:
R+(all real numbers)
or
(-infinity, infinity)
Range:
{ f+element R : -pi%2F2%3C=f%3C=pi%2F2 }
[-pi%2F2, pi%2F2]

answer: A)

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: Choice A
f(x) = sin(x)

-------------------------------------------------------

Reason:
The domain of sin(x) is "set of all real numbers"
In terms of notation we could write -infinity+%3C+x+%3C+infinity which further condenses to the interval notation
The domain of sine is this set of all real numbers because we don't have to worry about any input restriction for x.

The highest sin(x) can go is y = 1; the lowest is y = -1
We can then put a restriction on y to say -1+%3C=+y+%3C=+1
We get the interval notation for the range to be [-1, 1]
Use square brackets and NOT curved parenthesis here.
Square brackets include the endpoint.
Your teacher has made a typo when s/he wrote "range (-1,1)" as it should be "range [-1,1]".

A graph of y = sin(x) can verify the answer
graph%28400%2C400%2C-15%2C15%2C-5%2C5%2C-100%2Csin%28x%29%29
Desmos and GeoGebra are two handy graphing tools I use all the time. Both are free.
The graph above shows the domain being the set of all real numbers. It stretches forever to the left and right.
The curve is also between y = -1 and y = 1 inclusive to visually confirm the range is [-1,1].

If you were to graph something like y = tan(x), then you should note the infinitely many vertical asymptotes.
Each asymptote points to a restriction in the domain, i.e. an x value that needs to be kicked out of the domain.
This rules out choice C.
Choices B and D can be eliminated using similar logic.