Precalc Ch 4 Review

Domain and Range

100

Find the domain of f(x) = (2x-4)^(1/5)

(-inf , inf)

200

f(x) has a HA at y = 12. What is its range?

(-inf, 12) (12, inf)

300

The graph of f has a VA at x = 0. Give the new domain if y = f(x +1) - 4

(-inf, -1) (-1, inf)

400

Find the domain of y = -sqrt(3x-2)

(-inf, 2/3]

500

Find the domain of y = sqrt( x^2 - 81)

[-9 , 9]

Holes/Asymptotes

100

Given y = (x+1)/(x^2+3x +1). Find VA, HA, holes

hole x = -1 VA: x = -2 HA: y = 0

200

Write a function that has a hole when x = 0 , VA at x = 1/2 and HA at y = 0

Sample answer: y = x / (x(2x-1))

300

Given y = (3x^2 - 6x)/ (x-2) , find holes, VA , HA

hole x = 2 NO ASYMPTOTES

400

Given f(x) = 2x/(2x^2 +x) , find VA, HA, holes

hole at x = 0 VA: x = -1/2 HA: y = 1

500

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

hole x = 3/2 VA: x = -1 HA: y= 1

Solving Rational Functions

100

What is the LCD for 1 = (x+2)/(x-4) + (7x-42)/(x^2-4x))

x(x-4)

200

Solve( 1/(x-8) )- 1 = 7/(x - 8)

x = 2

300

Solve 1/6x^2 + 1/6x = 1/x^2

x = 5

400

Solve (5/(x-6)) - (4/(x+4)) = 3x / (x^2 - 2x - 24)

x = 22

500

Solve 3x/(x^2 - 3x) - (x-1)/(3-x) = 1

No Solution :)

Solving Root Functions

100

Solve 7 = sqrt(x - 1) + 4

x = 10

200

Solve x^(3/2) + 1 = 28

x = 9

300

sqrt(3x -11) = sqrt (5 - x)

x = 4

400

Solve 4throot(2x + 1) = sqrt (x - 1)

x = 4

500

2 = sqrt(3x - 2) - sqrt(10 - x)

x = 6

No Calculator

100

(8)^(-2/3)

1/4

200

3rdroot(64) * (9)^(-1/2)

4/3

300

3rdroot(27x^6y^9) * (6x^2y^3)^-1

1/2

400

( (6x^2y)^2 / sqrt(81x^4y^6) ) ^-1

y / 4x^2 OR 1/4 * y/x^2

500

3rdroot( x * sqrt(x)) * x^(-1/2)

1