Transcribed Text
Week 1: Equations and Inequalities
W1.1
Group Members who worked on this problem:
Solve for x:
2
5
4
2
1
x x
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W1.2
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You are choosing between two health clubs. Club A offers membership for a fee of $70 plus a monthly
fee of $25. Club B offers a membership fee of $45 plus a monthly fee of $30.
a. Using variables of your choice, set-up an equation for each club’s membership cost.
Make sure your variables are defined clearly.
b. After how many months will the total cost at each health club be the same?
c. What will be the total cost for each club from part (b)?
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W1.3
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Simplify. Write the final answer in standard form.
12
4 8
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W1.4
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Solve the quadratic equation using factoring:10x
2 +x = 2
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W1.5
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Solve the equation by making an appropriate substitution: x
4–9x
2 = – 20
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Week 2: Functions and Their Graphs
W2.1
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Use the graph for the following functions to determine domain and range for the function. Express
each domain or range in set-builder notation as well as interval notation.
a. b. c. d.
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W2.2
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Part I. Given the following function, y = f(x), find the indicated values:
a. f(3)
b. f(-2)
c. f(0)
Part II. Given the function f (x) = – x
2 + 7x – 20, find the indicated values:
d. f(3)
e. f(-3)
f. f(0)
W2.3
Group Members who worked on this problem:
Use the graph of f to the
right to determine each of
the following. Where
applicable, use interval
notation. (Assume that
at each end, there is an
arrowhead)
a. intervals on which f is
increasing
b. intervals on which f is
decreasing
c. any relative maxima or
minima and the
numbers at which they
occur
The graph may not be exact.
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W2.4
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Determine whether each function is even, odd, or neither. Justify your answer.
a. f(x) = 5x
2 + x
4
d.
b. f(x) = x
4
– x
3
c. f(x) = -5x
5 + x
3
a.
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W2.5
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I’m thinking of a linear equation with slope equal to –4 that goes through the point (3,5). Determine the
following:
a. Equation for the line in slope-intercept form
b. What is the slope of the linear equation?
c. Determine the y-intercept for this linear equation
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Week 3: Transformations and Algebra of Functions
W3.1
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In the following functions, a basic common function, f(x), has undergone a transformation into
another function. For each of the following graphs, determine the equation for g(x).
𝑓(𝑥) = 𝑥
2 a. g(x) = b. g(x) = c. g(x) =
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W3.2
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Find the domain for the following functions. You may use either set-builder notation or interval notation.
2
2
. ( ) . ( ) 3 9
. ( ) . ( )
2 4 10
a f x x c h x x
x x b g x d j x
x x
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W3.3
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Given f (x) = –2x +2andg(x) = -x
2
-3x+ 4, find the following:
a.
f g
b.
f g
c.
f g
d.
f g/
(don’t forget to factor and simplify if possible)
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W3.4
Given f(x) = – 2x
2 + x -3and g(x)= -x - 2, find the following:
a.
f g(x)
b.
g f (x)
c.
g f (2)
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W3.5
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Given the function f (x) = -3x – 8, find the formula for the inverse, f
-1
.
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Week 4: Polynomial Functions
W4.1
Group Members who worked on this problem:
Consider the parabola to the right to
determine each of the following:
a. Explain whether the function
has a maximum value or
minimum value.
b. Determine the minimum or
maximum value and where it
occurs.
c. Identify the vertex.
d. Identify the axis of symmetry.
The graph may not be exact.
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W4.2
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An athlete whose event is the shot put releases the shot in such a manner that the height can be modeled
by 𝑓(𝑥) = −0.02𝑥
2 + 𝑥 + 5.75 , where x is the shot’s horizontal distance, in feet, from the point of
release. The graph is given below. Answers must be accurate within one inch; to obtain answers of
sufficient accuracy, you must use the equation.
a. What is the maximum height of the shot and how far from its point of release does this occur?
b. What is the distance of the throw? (Assume that the shot neither bounces nor rolls upon impact.)
c. From what height was the shot released?
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W4.3
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A company producing steel construction bars uses the function R(x) = -0.06x
2+10.2x -50 to model
the unit revenue in dollars for producing x bars. For what number of bars is the revenue at a maximum?
What is the unit revenue at that level of production?
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W4.4
Group Members who worked on this problem:
Consider the function
( ) 4 8 2
3 2
f x x x x
to determine each of the following:
a. The function’s end behavior
b. The x-intercept(s). Make sure to clearly state whether the graph crosses the x-axis OR touches
the x-axis and turns around at each intercept
c. The y-intercept
d. Does the graph have y-axis symmetry, origin symmetry, or neither? Make sure to explain.
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W4.5
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Given the polynomial f(x) = x4 - 34x
2 + 225, (a) use the Rational Zero Theorem (aka Rational Roots
Theorem) to determine a list of possible zeros. (b) In your own words, explain the meaning of this list.
How could you use this information?
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Week 5: Exponential and Logarithmic Functions
W5.1
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Suppose that you have $12,500 to invest over a 4 year period. There are two accounts to choose from:
4.5% compounded monthly or 4.3% compounded continuously.
a. Write the formula for the first account’s compound interest for n compoundings per year.
b. Write the formula for the account with continuously compounded interest.
c. Use the formulas and information above to solve for the balance of each investment after 3 years.
d. Which investment account offers a better return on your money?
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W5.2
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Condense and/or simplify each of the following expressions using a property of logarithms.
a. 𝒍𝒐𝒈𝟖𝟐
b. 𝒍𝒐𝒈𝟔
(𝒙
𝟐 − 𝟑𝟔)−𝒍𝒐𝒈𝟔
(𝒙 − 𝟔)
c. 𝒍𝒐𝒈 𝟐𝟓+ 𝒍𝒐𝒈 𝟒𝟎
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W5.3
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Solve for x. Be sure to check your solution(s).
log(5 5) log(2 3) log(15) x x
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W5.4
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The Concord Community Park Association receives a $10,000 donation from an anonymous donor who
stipulates that before using the funds to improve the park, they must invest the money until it has doubled
in value. The Park Association decides to invest the money in an account that pays 7%, compounded
quarterly.
a. Write an equation that models the growth in value of the donation over time.
b. How many years will it take for the initial donation to double?
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W5.5
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A particular species of rare jungle bird is in danger of extinction. Fifteen years ago, the population was
18,500 and has been decreasing exponentially (A = A0e
kt). Today only 5,600 of the reptiles are alive.
a. Identify the exponential growth equation that models the population over time.
b. Using this equation, how many birds would we expect to be alive twenty years from now?
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Week 6: Systems of Equations and Inequalities
W6.1
Group Members who worked on this problem:
Solve each system of equations or indicate that it has no solution. You may use either the substitution
method or the addition method. Be sure to discuss the reasoning behind your choice of method(s).
a. {
2𝑥 +18𝑦 = −128
12𝑥 + 6𝑦 = 48
b. {
𝑦 = 2𝑥 − 4
9𝑥 + 3𝑦 = −72
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W6.2
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The Soccer Boosters club sells hotdogs and hamburgers at the games to raise funds for the soccer team.
Chili Cheese Hotdogs sell for $3.00 and hamburgers sell for $2.50. At the game last week 175 people
purchased a chili cheese hotdog or hamburger and exactly $480 was collected. How many of each was
sold?
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W6.3
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A company that manufactures a special brand of road bicycle has $200,000 in fixed expenses to produce
a new brand of bicycle. Each bicycle produced can be sold for $1350 and costs $650 to make. Let x
represent the number of bicycles made in the first year.
For this business venture:
a. Write the cost function, C(x).
b. Write the revenue function, R(x).
c. Determine the break-even point. Describe what this means.
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W6.4
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Timmy enjoys playing old-fashioned video games. He found 3 game systems on eBay and wants to
purchase a Nintendo game system, an Atari game system, and a Sega arcade game system. The Sega
system costs $600 more than the sum of the Atari and the Nintendo systems. All together, the three
game systems cost $11,000. The Atari system costs $1100 less than the Nintendo. Determine how
much Timmy paid for each game system.
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W6.5
Group Members who worked on this problem:
Give the algebraic representation of the system of inequalities
corresponding to the graph.
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These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.