Graph Rational Functions

x = -3

(-3,2)

x = -5

(3,8)

Crossing the x-axis

An absence of dirt.

Crossing a vertical asymptote.

A factor that cancels out.

Subtract 2 to from x, multiply the y by 5, then add 7 to y.

multiply the x by 5, add 2 to the x, then add 7 to the y.

subtract 2 from x and add 7 to y.

Add 2 to the x , multiply the y by 5, then add 7 to y.

x=1

x=-3

y=1

y= -3

x=1

x=-3

y=1

y= -3

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

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

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

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

 $y=\frac{3}{x-5}-14$  

 $y=\frac{3}{x+5}+14$  

 $y=\frac{3}{x-14}-5$  

 $y=\frac{3}{x+14}+5$  

 $\left(-\infty,-3\right)U\left(-3,\infty\right)$ 

 $\left(-\infty,1\right)U\left(1,\infty\right)$  

 $\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$  

All Real Numbers

x=1

x=-1

y=1

x=0

 $\left(-\infty,-3\right)U\left(-3,\infty\right)$ 

 $\left(-\infty,1\right)U\left(1,\infty\right)$  

 $\left(-\infty,-3\right)U\ \left(-3,\ 1\right)\ U\left(1,\infty\right)$  

All Real Numbers