Week 1: Equations and Inequalities W1.1 Group Members who worked ...

Week 1: Equations and Inequalities W1.1 Group Members who worked on this problem: Solve for x: 2 5 4 2 1 x  x  Calculations Explanations of Calculations Instructor Feedback: W1.2 Group Members who worked on this problem: 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)? Calculations Explanations of Calculations Instructor Feedback: W1.3 Group Members who worked on this problem: Simplify. Write the final answer in standard form. 12  4  8 Calculations Explanations of Calculations Instructor Feedback: W1.4 Group Members who worked on this problem: Solve the quadratic equation using factoring:10x 2 +x = 2 Calculations Explanations of Calculations Instructor Feedback: W1.5 Group Members who worked on this problem: Solve the equation by making an appropriate substitution: x 4–9x 2 = – 20 Calculations Explanations of Calculations Instructor Feedback: Week 2: Functions and Their Graphs W2.1 Group Members who worked on this problem: 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. Calculations Explanations of Calculations Instructor Feedback: W2.2 Group Members who worked on this problem: Calculations Explanations of Calculations Instructor Feedback: 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. Calculations Explanations of Calculations Instructor Feedback: W2.4 Group Members who worked on this problem: 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. Calculations Explanations of Calculations Instructor Feedback: W2.5 Group Members who worked on this problem: 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 Calculations Explanations of Calculations Instructor Feedback: Week 3: Transformations and Algebra of Functions W3.1 Group Members who worked on this problem: 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) = Calculations Explanations of Calculations Instructor Feedback: W3.2 Group Members who worked on this problem: 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        Calculations Explanations of Calculations Instructor Feedback: W3.3 Group Members who worked on this problem: 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) Calculations Explanations of Calculations Instructor Feedback: 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) Calculations Explanations of Calculations Instructor Feedback: W3.5 Group Members who worked on this problem: Given the function f (x) = -3x – 8, find the formula for the inverse, f -1 . Calculations Explanations of Calculations Instructor Feedback: 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. Calculations Explanations of Calculations Instructor Feedback: W4.2 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: W4.3 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: 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. Calculations Explanations of Calculations Instructor Feedback: W4.5 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: Week 5: Exponential and Logarithmic Functions W5.1 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: W5.2 Group Members who worked on this problem: 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 Calculations Explanations of Calculations Instructor Feedback: W5.3 Group Members who worked on this problem: Solve for x. Be sure to check your solution(s). log(5 5) log(2 3) log(15) x x     Calculations Explanations of Calculations Instructor Feedback: W5.4 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: W5.5 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: 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 Calculations Explanations of Calculations Instructor Feedback: W6.2 Group Members who worked on this problem: 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? Calculations Explanations of Calculations Instructor Feedback: W6.3 Group Members who worked on this problem: 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. Calculations Explanations of Calculations Instructor Feedback: W6.4 Group Members who worked on this problem: 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. Calculations Explanations of Calculations Instructor Feedback: W6.5 Group Members who worked on this problem: Give the algebraic representation of the system of inequalities corresponding to the graph. Calculations Explanations of Calculations Instructor Feedback: