RATIONAL FUNCTIONS

Asymptotes!

100

The asymptote of the function 3x³/x+8.

x = - 8

Infinite Discontinuity 

200

Name the types of asymptotes.

Horizontal Asymptote 

Vertical Asymptote

Oblique/Slant Asymptote

300

The asymptote(s) of the reciprocal function 1/f(x), where f(x) is x² - 4.

y = 0

x = 2

x = -2

400

The asymptote of the function f(x) = x³ + 27 / x + 3 

x = -3 

Hole/Removable Discontinuity 

500

The asymptote(s) of the function f(x) = x³ + 8 / x² - 4 

x = 2 

x 

Infinite Discontinuity 

Oblique/Slant Asymptote

General!

100

The limit as x approaches 3 for the function f(x) = 3x/x-3

DNE 

200

The domain and range of the following function: 

f(x) = 2x / x

Domain: All real numbers, x =/ 0

Range: All real numbers

300

The limit as x approaches -2 for the function x² - 4 / x+2

- 4 

400

The asymptote of f(x) = x^2 +8 / x.

y = x 

oblique

500

The rule to find a horizontal asymptote

If the numerator is greater than the denominator, there is no horizontal asymptote. 

If it is equal, it is the ratio between the coefficients. 

If it is less than, it is at y = 0

Definitions/Rules!

100

When any number is divided by 0, it is called this.

Undefined

200

The technical definition of a rational function. 

A rational fraction with a polynomial, f(x), in the numerator, and another polynomial, q(x), in the denominator. 

300

Give the technical term for expressions 0/0, infinity/infinity, and infinity⁰.

Indeterminate 

400

The several types of discontinuities.

Infinite, Hole, Jump

500

The rule to find an oblique asymptote.

If the degree of the polynomial inside the numerator is exactly one greater than the degree of the denominator's polynomial, there will be an oblique asymptote.

Example: x³ +8 / x²