Problem Set - November 1st
1. Find the domain of each, using set builder notation.
2. Given f(x) = x + 1 and g(x) = x2 + 2x, find the value of x such that f(g(x)) = 0
Problem Set - November 2nd
1. Given f(x) = -x2 + 5x - 2 and g(x) = 7x + 1
find
Problem Set - November 3rd
Using the composition of functions, prove f(x) and g(x) are inverse functions.
Find the inverse of f(x).
Problem Set - November 7th
Given the graph of f(x).
a. Graph the inverse and label appropriately.
-1
b. State the x-intercept of f (x).
-1
c. State the y-intercept of f (x).
-1
b. Evaluate f (1)
Problem Set ­ November 9th Given f(x) as shown in the graph.
f(x)
State the domain of f(x).
State the range of f(x).
Find f(­2)
Evaluate: 4f(­11) ­ 5f(4)
Find all integer values of x such that f(x) = 2.
Draw the sketch of f(x) + 3
Draw the sketch of f(x ­ 1). State the y ­ intercept of f(x ­ 1)
f(x) is a multi­defined or piecewise function, the first piece (in blue) of the graph is a linear, write the equation of the linear portion shown within the domain [­13,­8].
1
Problem Set - November 17th
1. Algebraically, find all values of x such that f(x) = g(x) given
f(x) = 4x2 - 13x + 2 and g(x) = x2 + 3x + 14.
2. State the domain of h(x), using interval notation, given
November 28th - Problem Set
1. Factor completely and state the zeroes of the corresponding equation.
2
2
2
2
-5x(9 - x ) - 14(9 - x ) + x (9 - x )
2. State the end behavior for the following functions.
3
2
a. f(x) = -5x + 7x + x + 2
6
5
4
3
2
b. g(x) = x - x + 2x - x + 3x - x + 4
Problem Set - November 29th
Write a fourth degree equation, with integer coefficients, with roots of 1/4, 2, -1 and -1/2.
Problem Set - December 1st
1. In chemistry, you learn about the ideal gas law (Boyle's Law) that tells you how gases
behave in terms of temperature, pressure and volume. If the temperature is held
constant, volume and pressure vary inversely. If the temperature is held constant and the
pressure is doubled, what happens to the volume?
2. m and n vary inversely. When m = 11, n = 5 and when m = (x + 3), n = (x + 9), find all
values of x that satisfy this situation and state the constant of proportionality. Only an
algebraic solution will be accepted for full credit.
3. y varies directly as the square of x. Given the ordered pairs (2, 3) and (5, j), find j.
2
Problem Set - December 5th
Solve the system.
Problem Set - December 15th
1. State the end behavior of the function.
3
2
a. f(x) = -7x + 9x + 3x - 8
4
3
2
b. g(x) = 8x - 11x + 2x - 3x + 17
How many zeroes does the function have?
State the zeroes.
3
2
f(x) = x + 2x - 25x - 50
Problem Set - December 16th
1. To balance a seesaw, the distance, in feet, a person is from the fulcrum is
inversely proportional to the person's weight, in pounds. Bill, who weighs 150
pounds, is sitting 4 feet away from the fulcrum. If Dan weighs 120 pounds, how
far from the fulcrum should he sit to balance the seesaw?
2. c and d vary inversely. When c = 20, d = 1/2 and when c = (x - 5),d = (x - 8),
find the constant of proportionality and all values of x. Only an algebraic
solution will earn full credit.
Problem Set - December 19th
2
2
1. Given f(x) = 4x - 11, g(x) = -x + 2x and h(x) = 2x + 5x - 18, find:
a. g(4)
b. f(h(1))
d. g(x) + h(x)
c. g(f(x))
e. f(x) * h(x)
Problem Set - December 20th
1. The revenue, R, in dollars, for selling x units of a product is 5.15x. The
cost, C, in dollars, for producing x units of the product is
C = 2.75x + 43.20.
a. Determine the slope and y-intercept of the cost equation, C, and
determine the meaning of each, in the context of the question.
b. How many units must be sold to break even (the cost is equal to the
revenue at the break-even point)?
c. Profit is defined as the revenue minus the cost. Determine the
equation for the profit.
d. What is the minimum number of units that must be sold to make a
profit $200?
2. Given the two functions shown, determine the average rate of change for f(x)
and g(x) over the interval [-3,4 ].
Which function has the steepest change (therefore the greatest average rate of
change)?
f(x) = -3x3 + 8x2 + 2x + 7
x
-3
-2
-1
0
1
2
3
4
g(x)
121
31
5
1
1
11
61
205
3