Rational Graph Characteristics

(1,0)

(-1,0)

(0,1)

(0,-1)

 $\left(0,-3\right),\ \left(0,\ 1\right)$  

 $\left(-5,\ 0\right)$  

 $\left(0,\ -5\right)$  

 $\left(-3,\ 0\right),\ \left(1,\ 0\right)$  

 $\left(0,\ \frac{1}{2}\right)$  

 $\left(\frac{1}{2},\ 0\right)$  

 $\left(-3,\ 0\right)$  

 $\left(0,\ -3\right)$  

(4, 0) and (0, -4)

(-4, 0) and (0, -4)

(-4, 0) and (0, 4)

(0, 0) and (0, -4)

x = -3

y = -3

x = -1

y = -1

x = -3

x = -5

x = -2

x = 3

x = 2

x= -5

x= 5

x= 6

x= -6

x = 0, -5

x=0, 5

x = 2, -7

x = -2, 7

y = -3

x = 1

y = -1

y=3

y = -3

x = 1

y = -1

y=3

Num = 4 Denom = 1

Num = 1 Denom = 1

Num = 1 Denom = 2

Num = 0 Denom = 1

y=4

y=0

y=-2

y=1

y = -4

y = 1

x = 1

y = -6

None

y=-2

y=2

y=0

 $\left(-\infty,\ \infty\right)$ All Reals

 $\left(-3,\infty\right)$ x-values bigger than -3

 $\left(-\infty,3\right)U\left(3,\infty\right)$ All reals but x $\ne$  3

 $\left(-\infty,-3\right)U\left(-3,\infty\right)$ All reals but x $\ne$   -3 

 $\left(-\infty,\ \infty\right)$ All Reals

 $\left(0,\infty\right)$ y-values bigger than 0

 $\left(-\infty,0\right)U\left(0,\infty\right)$ All Reals but y $\ne$   0

 $\left(-\infty,-3\right)U\left(-3,\infty\right)$ All reals but y $\ne$  -3 

D : All reals but x ≠ -3

R: All reals but y≠ 1

D : All reals but x ≠ 1

R: All reals but y≠ -3

D : All reals but x ≠ 3

R: All reals but y≠ 1

D : All reals but x ≠ -1

R: All reals but y≠ 3