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Type of Variation
Variation Word Problems
Solving Square Root Functions
Graphs and their Features
Exponential/ Radical Form
100
For this function, determine the type of variation and the constant of proportionality. y = -16x^2
What is Direct Variation. COP = -16.
100
Create a direct or inverse equation to model the situation, then solve the equation: 6 people can do a job in 10 hours. How long will it take 9 people to do the same job?
What is t = 60n t = 6 hours and 40 min
100
Solve each equation. Remember to check for extraneous solutions! 10 = sqrt(m/10)
What is m = 1,000. No E.S.
100
Graph the following and state the domain and range: y = sqrt(x)
What is Domain: x is greater than or equal to 0. Range: y is greater than or equal to 0.
100
Convert between rational and radical form. (2b)^1/2
What is sqrt(2b)
200
For the following function, determine the type of variation and the constant of proportionality. R(t) = 8/t
What is Inverse Variation. COP = 8
200
Create a direct or inverse equation to model the situation, then solve the equation: A pump empties a swimming pool in 40 minutes at the rate of 1400 L/min. If the rate of pumping is 2000 L/min, how long does it take to empty the swimming pool?
What is t = 56,000/r t = 28 minutes
200
Solve each equation. Remember to check for extraneous solutions! -8 + sqrt(5a-5) = -3
What is a = 6. No E.S. but what's weird about the square root part???
200
Graph the following function and state the domain and range. y = sqrt(x) = 7
What is Normal graph moved up 7 units. Domain: x is greater than or equal to 0. Range: y is greater than or equal to 7.
200
Convert between rational and radical form: (3root(2v))^5
What is (2v)^5/3
300
For the following equation, determine the type of variation and the constant of proportionality: z = -.2/t
What is Inverse Variation. COP = -.2
300
Suppose that y is inversely proportional to x, and that y = 0.4 when x = 2.5. Find y when x = 4.
What is y = .25 or 1/4
300
Solve the equation. Remember to check for extraneous solutions! 10sqrt(9x) = 60
What is x = 4. No E.S.
300
Graph the following function, then state the domain and range. y = 1/2sqrt(x) BONUS: How is the rate of this graph changed???
What is Graph is half as "tall". Domain: x is greater than or equal to 0. Range: y is greater than or equal to 0. BONUS: It increases at half the rate.
300
Convert between rational and radical form: (7p)^4/3
What is 3root(7p)^4
400
Write an equation that relates y and x inversely, and x = 10 when y = 5.
What is y = 50/x.
400
Create a direct or inverse equation to model the situation, then solve the equation: The volume of a gas varies inversely with the pressure of the gas on its container. If a pressure of 25 pounds per square inch corresponds to a volume of 68 cubic inches, What pressure is needed to correspond to a volume of 80 cubic inches?
What is P = 1700/V P = 21.25 Pounds Per Square Inch
400
Solve the equation. Remember to check for extraneous solutions! sqrt(30-x) = x
What is x = -6 and x = 5 No E.S.
400
Graph the following function. Then state the domain and range: y = sqrt(x-2) + 3
What is Graph is shifted right two and up 3. Domain: x is greater than or equal to 2. Range: y is greater than or equal to 3.
400
Determine if the two sides of the equation are equal. If not, how can you change it to make it equal? 3root(64) = 16^1/2
What is True!
500
Write an equation that relates y and x inversely such that y = 10/9 when x =9.
What is y = 10/x
500
The volume of a sphere varies with its radius. If two solid spheres with radius 2 m and 4 m respectively are melted and reformed into one sphere then find the diameter of the new sphere HINT: V= kr^3
What is Find volume of two spheres combined and solve for r: 72k = k R^3 R^3 = 72 = 4.16 approximately.
500
Solve the equation. Remember to check for extraneous solutions! r = (-1-2r)^1/2
What is r = -1. No E.S. but why????
500
Graph the following function, then state the domain and range. y = -3sqrt(x-3)+2
What is Graph is flipped upside down, 3 times as "tall or wide", shifted right 3 and moved up 2. Domain: x is greater than or equal to 3. Range: y is less than or equal to 2.
500
Determine if the two sides of the equation are equal. If not, how can you change them to make them equal? 27^1/2 = sqrt(3^2)
What is Change 27 to the 1/3 power