Rational Functions

Graphing Rational Functions

100

Graph: f(x) = (2x)/(x^2 - 1)

What is H.A. y = 0 V.A. x = -1, x = 1 Holes: None

200

Graph: f(x) = 8/(x^2 - x - 6)

What is H.A. y = 0 V.A. x = 3, x = -2 Holes: Nones X-int. None

300

Graph: f(x) = (x^2 - 9)/(x^2 - 2x - 15)

What is H.A. y = 1 V.A. x = 5 Holes: x = -3 x-int: x = 3

400

Graph: f(x) = (x^2 + 3)/(2x^3)

What is H.A. y = 0 V.A. x = 0 Holes: None x-Int: None

500

Graph: f(x) = (x^2 - 5x - 36)/(3x)

What is HA: none VA: x = 0 Holes: none x-int: x = -4, x = 9

Variation

100

If y varies inversely with x and y = 3 when x = 8, find y when x = -4.

What is -6

200

If y varies directly with x, and y = 12 when x = 2, find y when x = 7.5

What is 45.

300

Write an equation if w varies inversely with y and jointly with x and z.

What is w = xz/y

400

Write an equation if y varies jointly with x and the square of z.

What is y = xz^2

500

Suppose x varies inversely with y, and y varies inversely with z. How does x vary with z? Prove it.

What is directly. x = a/y y = b/z x = a/(b/z) so x = (a/b)z

Multiplying Rational Expression

100

(5*x^3*y)/(x^2*y^2) times (y^3)/(15*x^2)

(y^2)/(3x)

200

(x(x-3))/(x-2) times (x+3)(x-2)/(x)

(x^2-9)

300

(3x-12)/(x+5) times (x+6)/(2x-8)

(3(x+6))/(2(x+5))

400

(x^2+3x-4)/(x^2+4x+4) times (2x^2+4x)/(x^2 - 4x+3)

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

500

(x^2+5x-36)/(x^2 - 49) times (x^2 - 11x+28)

(x+9)(x-4)^2 / (x+7)

Dividing Rational Expression

100

(5*x^2*y^3)/(x^7) divided by (30*x*y^4)/(y^3)

(y^2)/(6x^6)

200

(x+3)(x-2)/(x(x+1)) divided by (x+3)/(x)

(x-2)/(x+1)

300

(x^2 - 6x - 27) / (2x^2+2x) divided by (x^2-14x+45)/(x^2)

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

400

(3x^2+13x+4)/(x^2 - 4) divided by (4x+16)/(x+2)

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

500

(x^2 - 8x+15)/(x^2+4x) divided by (x^2 - x - 20)

(x-3)/(x(x+4))^2

Solving Rational Equations

100

5/x = x/5

x=5 and -5

200

(x - 4)/3 = (x-2)/2

x = -2

300

1/(4 - 5x) = 3/(x + 9)

x = 3/16

400

2/(6x+2) = x/(3x^2 + 11)

x = 11

500

(6y - 20) / (y - 5) = 8 / (y - 5)

y = 14/3