Chapter 7 and 8 Review

Asymptotes of Rational Functions

100

What is the VA for f(x) = (2x+3) / (x-4)

x = 4

200

This is the horizontal asymptote of the function f(x) = (x - 3)/(x + 4).

What is y = 1?

300

What is the VA for f(x) = (6x²-1) / (2x+5)

x = -5/2

400

What is the HA for f(x) =       1 / (2x-3)

y = 0

500

What is the VA for f(x) =     (x²-1) / (x+1)

None

More Graph Details

100

What is the y-intercept for f(x) = (x-3) / (x+3)

y = -1

200

This is the x-intercept of the function f(x) = ((x + 2)(x - 1))/(x - 1).

What is x = 1?

300

What is the hole for f(x) = (x²-1) / (x+1)

x = -1

400

What is the hole for f(x) = (x²-4x+4) / (x²-3x+2)

x = 2

500

This is a hole in the graph of the function f(x) = ((x + 1)(x - 2)(x + 3))/((x + 3)(x - 2)).

What is x = -3 and x = 2?

Multiplying and Dividing

100

(7x/(2x-10)) divided by (x^2-6x)/(x^2-11x+30)

7/2 x cannot equal 5, 0, 6

200

(6x^2+x-15)/4x^2 divided by (3x^2+5x)

(2x-3)/4x^3 x cannot equal 0 and -5/3

300

(x^2-3x)/(x-2) TIMES (x^2+x-6)/x

x^2-9 x cannot equal 2 and 0

400

(3x^2+13x+4)/(4x^2-16) Divided by (8x+32)/(4x+8)

(3x+1)/(8x-16) x cannot equal -2,-4,2

500

(4x^2+20x)/(x^3+4x^2) TIMES (x^2+8x+16)/(8x^2+36x-20)

(x+4)/(2x^2-x) x cannot equal 0,-4,-5,1/2

Adding and Subtracting

100

5x/(x+3) + (15/(x+3))

5 x cannot = -3

200

Find the LCM of the polynomials: 24x^2 and 8x^2-16x

24x^2(x-2)

300

(x+4)/(x^2-4) - (15/(x-2))

(-14x-26)/(x+2)(x-2)

400

(x^2-5)/(x^2+5x-14) - ((x+3)/(x+7))

(-x+1)/(x+7)(x-2) x cannot equal -7 or 2

500

(x+2)/(x-4) + 2/x + 5x/(3x-1)

(8x^3-9x^2-28x+8)/(x(x-4)(3x-1))

Equations

100

4/x + x = 5

x = 1 and 4

200

2/3x + 1/6 = 4/3x

x=4

300

(x-3)/(x+5) = x/(x+2)

x = -1

400

(x-1)/x + (2x-1)/(x+3) = (x+6)/ (x+3)

x = -.5 and 3

500

3x/(x+1) = 12/(x^2-1) + 2

x = -2 and 5