Graphing Rational Functions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Solving Rational Equations
Rational Function Word Problems
100
What is the domain and range of the function below in interval notation?
y = 1/x
Domain:
(-oo, 0)U(0, oo)
Range:
(-oo, 0)U(0, oo)
100
Find the product and list excluded values:
(2x^2 - 10x)/(x^2 - 25) * (x + 3)/(2x^2)
(x + 3)/(x(x + 5)
x != -5, 0, 5
100
Simplify and list excluded values:
4/x + 7/(6x^2)
(24x + 7)/(6x^2)
x!= 0
100
Solve:
15/x + 4/5 = 7/x
x = -10
100
It takes Rosemary 5 minutes to finish a bag of Skittles by herself. It takes Katherine 8 minutes to finish a bag of Skittles herself. How long would it take them to finish the bag if they shared the bag? Round to the nearest tenth, and include units!
3.1 minutes
200
What are the asymptote equations of the following function?
y = -1/(x - 2) + 1
x = 2, y = 1
200
Find the product and list excluded values:
(3x^5y^2)/(8xy)*(6xy^2)/(9x^3y)
(x^2y^2)/4
x !=0, y!= 0
200
Simplify and list excluded values:
7 - 4/(x - 9)
(7x - 67)/(x - 9)
x!= 9
200
Solve:
1/(2x + 5) = x/(11x + 8)
x = -1, 4
200
It takes Mrs. G.A. twelve days to build a dog house. When she is working together with her dad, it takes them only 5 days to build a dog house. How long would it take Mrs. G.A.'s dad to build the dog house by himself? Round your answer to the nearest tenth and include units!
8.6 days
300
What are the asymptote equations of the following function?
y = (-2x + 3)/(x + 5)
x = -5, y = -2
300
Find the product and list excluded values:
(x + 3)/(x^3 - 1) * (x^2 + x + 1)
(x + 3)/(x - 1)
x!= 1
300
Simplify and list excluded values:
(3x - 2)/(x^2 + 2x - 24) - (x - 3)/(x^2 - 16)
(2x^2 + 7x + 10)/((x + 6)(x + 4)(x - 4))
x != -6, -4, 4
300
Solve:
(3x)/(x + 1) - 5/(2x) = 3/(2x)
x = -2/3, 2
300
It takes Lisa and Laura the same amount of time to get to the movie theater. Lisa lives 8 miles from the movie theater and Laura lives 12 miles from the movie. If Laura is driving 3 mph faster than Lisa, how fast is Laura driving?
9 mph
400
Sketch a graph of the function. List the asymptote equations as well as two exact coordinates.
y = -3/x - 4
x = 0, y = -4
400
Find the quotient and list the excluded values:
(11x)/(3x - 9) -: (x^2 - 5x)/(x^2 - 8x + 15)
11/3
x != 0, 3, 5
400
Simplify and list excluded values:
2 + x/(x - 3) - 3/(x^2 - 9)
(3(x^2 +x - 7))/((x + 3)(x - 3))
x != -3, 3
400
Solve:
3/(x - 1) - 1 = 6/(x^2 - 1)
x = 2
400
A boat travels 12 miles going upstream in the same time it travels 20 miles going downstream. If the speed of the current is 5 miles per hour, what is the speed of the boat in still water? Don't forget to include units!
20 mph
500
Sketch a graph of the function below. List the asymptote equations of the function, as well as two exact coordinates.
y = (x - 7)/(x + 2)
x = 2, y = 1
(-1, -8), (-3, 10)
500
Find the quotient and list excluded values:
(6x^2 + 4x - 2)/(5x^2) -: (2x^2 + 2x)
(3x - 1)//(5x^3)
x!=0, -1
500
Simplify and list excluded values:
2/(x^2 - 5x + 6) - 4/(x^2 - 2x -3 ) + 2/(x^2 + 4x + 3)
(-6(x -7))/((x - 3)(x - 2)(x + 1)(x + 3))
x != 3, 2, -1, -3
500
Solve:
9/(x - 2) + (6x)/(x + 2) = (9x^2)/(x^2 - 4)
x = -3
500
A plane travels the 500 miles flying with the wind in the same time that it travels 375 miles against the wind. If the plane is traveling 550 miles per hour in still air, what is the speed of the wind? Round your answer to the nearest tenth and include units!
78.6 mph