Question

Choose the function that has:

Domain: x*-1
Range: y# 2
O
Ax)= x+2
x-1
O
2x+1
Ax)=
x+1
2x+ 1
(x) =
x-1

Answer 1

Given:

`Domain\\eq -1`

`Range\\eq 2`

To find:

The function for the given domain and range.

Solution:

A function is not defined for some values that makes the denominator equals to 0.

The denominator of functions in option A and C is
`(x-1)`.

`x-1=0`

`x=1`

So, the functions in option A and C are not defined for
`x=1` but defined for
`x=-1`. Therefore, the options A and C are incorrect.

In option B, the denominator is equal to
`x+1`.

`x+1=0`

`x=-1`

So, the function is not defined for
`x=-1`. Thus,
`Domain\\eq -1`.

If degree of numerator and denominator are equal then the horizontal asymptote is
`y=(a)/(b)`, where a is the leading coefficient of numerator and b is the leading coefficient of denominator.

In option B, the leading coefficient of numerator is 2 and the leading coefficient of denominator is 1. So, the horizontal asymptote is:

`y=(2)/(1)`

`y=2`

It means, the value of the function cannot be 2 at any point. So,
`Range\\eq 2`.

Hence, option B is correct.