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Course by: Pradnya Bhawalkar, Kim Johnston. E-mail the authors

# Putting It All Together - Graphing Rational Functions

Module by: Pradnya Bhawalkar, Kim Johnston. E-mail the authors

Summary: 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.

## Exercise 1

rx=x+1x(x+4) r x x 1 x x 4

### Solution

Domain: -4 -4 0 0 -4 -4 0 0

Hole: None

VA: x=0x0, x=-4x-4

HA: y=0y0

SA:None

Zero: (-1,0)

Y-int: None

## Exercise 2

hx=(2x2)(x3)(x1)(x+2) h x 2 x 2 x 3 x 1 x 2

### Solution

Domain: -2 -2 1 1 -2 -2 1 1

Hole: None

VA: x=-2x-2, x=1x1

HA:None

SA: y=2x8 y 2 x 8

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

Y-int: (0,0)

## Exercise 3

fx=3x+32x+4 f x 3 x 3 2 x 4

### Solution

Domain: -2 -2 -2 -2

Hole: None

VA: x=-2x-2

HA: y=32y32

SA: None

Zero: (-1,0)

Y-int: (0,3434)

## Exercise 4

gx=6x2x6 g x 6 x 2 x 6

### Solution

Domain: -2 -2 3 3 -2 -2 3 3

Hole: None

VA: x=-2x-2, x=3x3

HA: y=0y0

SA: None

Zeros: None

Y-int: (0,-1)

## Exercise 5

hx=2x+4x1 h x 2 x 4 x 1

Domain: 1 1 1 1

Hole: None

VA: x=1x1

HA: y=2y2

SA: None

Zero: (-2,0)

Y-int: (-2,0)

## Exercise 6

tx=3xx2+4 t x 3 x x 2 4

Domain:

Hole: None

VA: None

HA: y=0y0

SA: None

Zero: (0,0)

Y-int: (0,0)

## Exercise 7

fx=x2+4x24 f x x 2 4 x 2 4

### Solution

Domain: -2 -2 2 2 -2 -2 2 2

Hole: None

VA: x=-2x-2, x=2x2

HA: y=1y1

SA: None

Zeros: None

Y-int: (0,-1)

## Exercise 8

fx=xx+22 f x x x 2 2

### Solution

Domain: -2 -2 -2 -2

Hole: None

VA: x=-2x-2

HA: y=0y0

SA: None

Zeros: (0,0)

Y-int: (0,0)

## Exercise 9

fx=5x2x+3 f x 5 x 2 x 3

### Solution

Domain: -3 -3 -3 -3

Hole: None

VA: x=-3x-3

HA: None

SA: y=5x15 y 5 x 15

Zeros: (0,0)

Y-int: (0,0)

## Exercise 10

fx=x3x2+1 f x x 3 x 2 1

Domain:

Hole: None

VA: None

HA: y=0y0

SA:None

Zeros:(3,0)

Y-int: (0,-3)

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