Use the graph to help you decide if the following function has an inverse function or not:
f(x) = x^4
What is does NOT have an inverse function?
100
Find a mathematical model for the verbal statement:
A varies directly as r^2. (A = 9π (9 pi) when r = 3)
What is A = πr^2 ? ( A = pi * r squared)
100
Find the inverse of f(x) = (1/6)x.
What is (f^-1)(x) = 6x ?
100
Given f(x) = x^2 and g(x) = 1-x,
find (f - g)(x).
What is x^2 + x - 1 ?
200
Horizontal Line Test
What is a graphical test to determine the existence of an inverse function of f ?
200
Use the graph to help you decide, is the following function one-to-one?
f(x) = (3x+4)/5
What is yes?
200
Write the model for the following:
z is jointly proportional to the square of x and the cube of y
What is z = k x^2 y^3
200
Find the inverse of g(x) = (x-1)/7.
What is (g^-1)(x) = 7x + 1 ?
200
Given f(x) = x^2 + 6 and g(x) = x + 2,
find (fg)(x).
What is x^3 + 2x^2 + 6x +12?
300
Explain the role of y = x to inverses and their functions.
What is the reflection line for f and f^(-1)?
300
A function f is one-to-one if each value of the __________ variable corresponds to exactly one value of the _____________ variable.
What is dependent variable (or y-value) and the independent variable (or x-value)?
300
Determine the constant of variation for the following:
y is inversely proportional to x
( y = 7 when x = 4 )
What is k = 28 ?
300
Name the steps to find an inverse function once you have determined that the function is one-to-one.
What is Step 1: Replace f(x) with y.
Step 2: Interchange the x and y.
Step 3: Solve for y.
Step 4: Replace y with f^-1.
300
Given f(x) = x^2 + 1 and g(x) = (x - 4),
find (f/g)(5).
What is 26?
400
In the direct variation equation y = kx, the k.
What is constant of proportionality or constant of variation?
400
Use the graph of the following function to determine if it is one-to-one.
h(x) = l x - 2 l, for x < or = to 2.
What is yes?
400
The total cost of an item is directly proportional to the retail price.
Maddie lives in Tahlequah and has just purchased a pair of Skullcandy Knockout on-ear headphones that have a retail price of $99.99. Her total cost is $109.49.
Find the value of the constant of variation and then state the tax rate for Tahlequah.
What is k = 1.095 and a tax rate of 9.5% ?
400
Find the inverse of h(x) = √(2x + 3), for x greater than or equal to -3/2. State any restrictions.
What is (h^-1)(x) = (x^2 - 3) / 2, for x greater than or equal to 0.
400
Given f(x) = 3/(x^2 -1), for x not equal to 1 or -1 and g(x) = (x + 1),
find (f(g(x)).
What is 3/(x^2 + 2x) for x not equal to 0?
500
Mathematical models that involve both direct and inverse variation are said to have _____________ variation.
What is combined?
500
Use the graph of the following function to determine if it is one-to-one
f(x) = (x - 1)^(1/3)
What is yes?
500
The Oklahoma Department of Transportation is debating whether to change the speed limit on a highway from 60 mph to 75 mph. Use the following information to help them inform the public. The travel time between two cities is inversely proportional to the average speed.
A car travels between two cities in 2 hours and 30 minutes at an average speed of 60 mph. Find out how long it would take to travel between the two cities at an average speed of 75.
What is 2 hours ?
500
Given that h(x) = 9 - x^2, find (h^-1(h^-1(-7)).
What is √5 ?
500
Find two functions f and g such that (f(g(x)) is
h(x) = √(9-x).
Sample question as there are many correct questions:
What is f(x) = √x and g(x) = 9 - x ?