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Graphing rational functions.

When graphing rational functions, find the domain, vertical asymptotes, slant asymptotes, holes (if any), horizontal asymptotes, vertical asymptotes, zeros, and y-intercept.

To practice, graph each rational function. State the domain, hole(s), VA (vertical asyptote(s)), HA(horizontal asymptote), SA(slant asymptote), zeros, and y-intercept(y-int).

Use graph paper .

r x x 1 x x 4

Domain: -4 -4 0 0

Hole: None

VA: x 0 , x -4

HA: y 0

SA:None

Zero: (-1,0)

Y-int: None

h x 2 x 2 x 3 x 1 x 2

Domain: -2 -2 1 1

Hole: None

VA: x -2 , x 1

HA:None

SA: y 2 x 8

Zeros: (0,0), (3,0)

Y-int: (0,0)

f x 3 x 3 2 x 4

Domain: -2 -2

Hole: None

VA: x -2

HA: y 3 2

SA: None

Zero: (-1,0)

Y-int: (0, 3 4 )

g x 6 x 2 x 6

Domain: -2 -2 3 3

Hole: None

VA: x -2 , x 3

HA: y 0

SA: None

Zeros: None

Y-int: (0,-1)

h x 2 x 4 x 1

Domain: 1 1

Hole: None

VA: x 1

HA: y 2

SA: None

Zero: (-2,0)

Y-int: (-2,0)

t x 3 x x 2 4

Domain:

Hole: None

VA: None

HA: y 0

SA: None

Zero: (0,0)

Y-int: (0,0)

f x x 2 4 x 2 4

Domain: -2 -2 2 2

Hole: None

VA: x -2 , x 2

HA: y 1

SA: None

Zeros: None

Y-int: (0,-1)

f x x x 2 2

Domain: -2 -2

Hole: None

VA: x -2

HA: y 0

SA: None

Zeros: (0,0)

Y-int: (0,0)

f x 5 x 2 x 3

Domain: -3 -3

Hole: None

VA: x -3

HA: None

SA: y 5 x 15

Zeros: (0,0)

Y-int: (0,0)

f x x 3 x 2 1

Domain:

Hole: None

VA: None

HA: y 0

SA:None

Zeros:(3,0)

Y-int: (0,-3)

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Source:  OpenStax, "rational"ity. OpenStax CNX. May 03, 2006 Download for free at http://cnx.org/content/col10350/1.2
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