Domain of Rational Functions

The domain of a rational function is...

• the $x-$ values that make the denominator equal 0

• the range of possible $y-$ values the function reaches

• the range of acceptable $x-$ values that may be plugged into the function

• the $y-$ intercept

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

Find the domain of

 $f\left(x\right)\ =\ \frac{x-3}{x+4}$ . 

•  $\left(-\infty,\ \infty\right)$  

•  $\left(-\infty,3\right)\cup\left(3,\infty\right)$  

•  $\left(-\infty,-4\right)\cup\left(-4,\infty\right)$  

•  $\left(-\infty,-4\right)\cup\left(-4,3\right)\cup\left(3,\infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.5

Find the domain of

 $f\left(x\right)\ =\ \frac{x-1}{x^2+1}$ . 

•  $\left(-\infty,\ \infty\right)$  

•  $\left(-\infty,-1\right)\cup\left(-1,\infty\right)$  

•  $\left(-\infty,1\right)\cup\left(1,\infty\right)$  

•  $\left(-\infty,-1\right)\cup\left(-1,1\right)\cup\left(1,\infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

Select all  x-values are NOT in the domain of  $f\left(x\right)\ =\ \frac{x+2}{x\left(x^2+4\right)\left(x^2-25\right)}$  

•  $x=2$  

•  $x=-2$  

•  $x=5$  

•  $x=-5$  

•  $x=0$  

Tags

CCSS.HSF.IF.B.5

At the x-values that are NOT in the domain of a rational function, we usually see the function going up to infinity or down to negative infinity. What is the name of these "walls" of the graph, which the function cannot pass?

Tags

CCSS.HSF.IF.B.5

Select each of the following true statements about
 $f\left(x\right)\ =\ \frac{1}{\left(x+1\right)\left(x+3\right)}$ 

• As  $x\ \rightarrow\ -\infty$ ,  $f\left(x\right)\ \rightarrow\ \infty$   

• As  $x\ \rightarrow\ \infty$ ,  $f\left(x\right)\ \rightarrow\ 0$   

• As  $x\ \rightarrow\ -1$  from the right,  $f\left(x\right)\ \rightarrow\ -\infty$  

• As  $x\ \rightarrow\ -3$  from the left,  $f\left(x\right)\ \rightarrow\ -\infty$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.REI.D.10

How would you rate your understanding of this topic - domain of rational functions?

• Not confident at all - so lost!

• A little confused...

• Feeling okay, but need more practice.

• So easy, next topic please!

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.REI.A.2