Rational Functions

VAs

100

f(x)=(x-3)/(x+4)

x = -4

200

f(x)=(2x-3)/(3x-6)

x = 2

300

f(x)=(5x-4)/(7x-9)-3

x = 9/7

400

f(x)=(x-4)/(x² - 9)

x = 3 and x = -3

500

f(x) = (3x² - 4x -10)/(x² + 3x +2)

x = -1 and x = -2

HAs

100

f(x)=(x-3)/(x+4)

y = 1

200

f(x)=(2x-3)/(3x-6)

y = 2/3

300

f(x)=(5x-4)/(7x-9)-4

y = -23/7

400

f(x)=(x-4)/(x² - 9)

y = 0

500

f(x) = (3x² - 4x -10)/(x² + 3x +2)

y = 3

SAs

100

f(x) = (x² - 3x + 3)/(x - 1)

y = x - 2

200

f(x) = (x² - 16)/(x + 3)

y = x - 3

300

f(x) = (9x² + 3x +12)/(3x - 15)

y = 3x + 16

400

f(x) = (x² +5)/(2x + 4)

y = 0.5x - 1

500

f(x) = (x³ + x² - x + 1)/(x² +3x - 1)

y = x - 2

Graph It!

100

f(x)=6/(x+4)

VA:  x = -4

HA:  y = 0

200

f(x)=(x-3)/(x-6)

VA:  x = 6

HA:  y = 1

300

f(x)=(x-3)/(2x)+1

VA:  x = 0

HA:  y = 3/2

400

f(x) = (x² - 4x + 1)/(x - 2)

VA:  x = 2

SA:  y = x - 2

500

f(x) = (x² +3x)/(x+4)

VA:  x = -4

SA:  y = x - 1

Apps and PoDs

100

P(x) = (12000-150x)/(120 - x) represents the average health of a SIMS character as a percentage after x hours of game play.  Identify and explain the meaning of the vertical asymptote.

HA:  x = 120

The SIMS character lives a maximum of 120 hours.  (As the number of hours of game play approaches 120 hours, the health of the character approaches negative infinity.

200

P(x) = (12000-150x)/(120 - x) represents the average health of a SIMS character as a percentage after x hours of game play.  What is the average amount of time it takes for the SIMS character to die (health reaches 0%)?

x = 80 hours

300

You scored 18 out of 25 multiple choice questions correct on your Chem Midterm.  Write a function that models your Chem Midterm grade if the Free Response section is worth x points and you get all the points on the Free Response Section.

G(x)=(18 + x)/(25 + x)

400

Identify the PoD:  f(x) = (x² + 5x - 6)/(x + 6)

(-6, -7)

500

Identify the PoD:  f(x) = (x² - 4x + 4)/(x²  - 4)

(2, 0)