Rational Functions

Classifying/Zeros

100

Given the function, classify by degree and number of terms:

x³+2x

Cubic

Binomial

200

Given the function, classify by degree and number of terms:

x²-7x⁴+5

Quartic

Trinomial

300

Given the function, classify by degree and number of terms:

(x³-3)/(x^4+2x)

Not a polynomial function

400

Given the function, classify by degree and number of terms:

x⁶-3x²+4x

6th degree

Trinomial

500

Given the function, classify by degree and number of terms:

x³-5x⁵+7x²-1

Quintic

Polynomial

Asymptotes

100

Given the function, find the vertical asymptote(s)

(x³-2x²+8x)/(x+9)

VA @ x=-9

200

Given the function, find the horizontal asymptote

(x³-9x²+5x-1)/(x⁵+4x)

HA @ y=0

300

Given the function, find the vertical asympote(s)

(x²-x+8)/(x³-x²-6x)

VA @ x=0, 3, -2

400

Given the function, find the horizontal asymptote

(6x⁴-7x²+9)/(-2x⁴+3x³-10)

HA @ y=-3

500

Given the function, find the oblique asymptote

(-2x²+3x+1)/(x+2)

OA @ y= -2x+7

Factoring

100

Factor the function into simplest terms

(x²+8x-20)/(x-1)

[(x+10)(x-2)]/(x-1)

200

Factor the function into simplest terms

(x³+x²-6x)/(x²-16)

[x(x+3)(x-2)]/[(x+4)(x-4)]

300

Factor the function into simplest terms

(x³+5x²+4x)/(-4x²+4x)

[x(x+4)(x+1)]/[(-4x)(x-1)]

400

Factor the function into simplest terms

(7x²+5x-2)/(x+4)

[(7x-2)(x+1)]/(x+4)

500

Factor the function into simplest terms

(2x²-4x+8)/(3x²-27)

[2(x-2)(x-2)]/[3(x+3)(x-3)]

Parts of a Function

100

Given the function, simplify the function into lowest terms

(2x+6)/(x²+5x+6)

2/(x+2)

200

Using the function, identify the coordinate point of the hole

(2x+6)/(x²+5x+6)

Hole @ x=-3, y=-2

(-3,-2)

300

What is the domain of the function?

(2x+6)/(x²+5x+6)

D: {x l x =/ -3,-2}

=/ means does not equal

400

Given the function, identify the coordinate point of the hole

(x²+6x+8)/(x²+3x-4)

Hole at x=-4, y=2/5

(-4, 2/5)

500

Given the function, what are the x and y intercepts

(x²+6x+8)/(x²+3x-4)

x-intercept: x=-2

y-intercept: y=-2

Making a Function

100

Given the figure, what are the x-intercepts

x-intercepts: x=-2, 3

200

Given the figure, what are the factors given the x-intercepts

(x+2)(x-3)

300

Given the figure, what are the vertical and horizontal asymptotes

VA @ x=-1, 2

HA @ y=0

400

Given the figures, use the vertical asymptotes, create the proper factors

(x+1)(x-2)²

500

Given the function, create the approximate proper function

[(x+2)(x-3)]/[(x+1)(x-2)²]