Domain and Range of Rational Functions

In finding the domain of the rational function

 $r\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$  where p(x) and q(x) are polynomial functions, all real numbers are allowed for x except . . .
(Check all that applies.)

• The ones that would make the numerator zero. $p\left(x\right)=0$  

• The ones that would make the denominator zero.  $q\left(x\right)=0$  

• The ones that would make the function zero. $r\left(x\right)=0$  

• The ones that would make the function undefined.

What process do we have to do first in order to obtain the range of a rational function without the aid of its graph?

(Check all that applies.)

• Find the reciprocal of the function.

• Find the inverse of the function.
  

• Find the function x in terms of y.

• Find the solution of the function.

What is the domain of 

 $y=\frac{1}{x}$  ?

•  $x\ne-1$  

•  $x\ne0$  

•  $x\ne1$  

•  $x\ne y$  

What is the range of 

 $y=\frac{1}{x}$  ?

•  $y\ne-1$  

•  $y\ne0$  

•  $y\ne1$  

•  $y\ne x$  

Find the domain of 

 $y=\frac{2}{x+1}$  .

•  $x\ne-1$  

•  $x\ne0$  

•  $x\ne1$  

•  $x\ne2$  

Find the range of 

 $y=\frac{2}{x+1}$  .

•  $y\ne-1$  

•  $y\ne0$  

•  $y\ne1$  

•  $y\ne2$  

The domain of 

 $y=\frac{x-1}{x+2}$  is

•  $x\ne-2$  

•  $x\ne-1$  

•  $x\ne1$  

•  $x\ne2$  

The range of 

 $y=\frac{x-1}{x+2}$  is

•  $y\ne-2$  

•  $y\ne-1$  

•  $y\ne1$  

•  $y\ne2$  

What is the domain of 

 $y=\frac{\left(x-1\right)\left(x+4\right)}{\left(x+2\right)\left(x-3\right)}$ ? (Check all that applies.) 

•  $x\ne-2$  

•  $x\ne-1$  

•  $x\ne3$  

•  $x\ne4$  

Find the range of 

 $y=\frac{x^2+5x+6}{x+2}$  .

•  $y\ne-2$  

•  $y\ne-1$  

•  $y\ne1$  

•  $y\ne2$