Question

Choose the function that has:

Answer 1

Given:

$Domain\neq -1$

$Range\neq 2$

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, $Domain\neq -1$.

If degree of numerator and denominator are equal then the horizontal asymptote is $y=\dfrac{a}{b}$, 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:

$y=\dfrac{2}{1}$

$y=2$

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

Hence, option B is correct.