Chapter 8 Review
Non-Calculator Portion
8-1 Inverse Variation
1. Suppose x and y vary inversely. Write a function that models each inverse variation. Then find y when x=10.
a. x=7 when y=2
b. x=4 and y=0.2
c. x=4.75 and y=4
2. Is the relationship between the values in each table an inverse variation? If it is, write an equation to model the relationship.
a.
x / 1 / 3 / 7 / 10y / 2 / 8 / 20 / 29
b.
x / 3 / 1.5 / 0.5 / 0.3y / 5 / 10 / 30 / 50
c.
x / / / / 2y / 31 / 7 / 3 /
8-2 The Reciprocal Function Family
Graph using transformations. Then list the domain and range.
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8-3 Rational Functions and Their Graphs
Graph each rational function. Find the domain and list all points of discontinuity.
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8-4 Rational Expressions
Multiply. State any restrictions on the variables.
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Divide. State any restrictions on the variable.
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8-5 Adding and Subtracting Rational Expressions
Simplify each sum or difference. State any restrictions on the variables.
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8-6 Solving Rational Equations
Solve each equation. Check each solution.
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Calculator Portion
8-1 Inverse Variation
22. Your employer decides to hire extra help to deliver newspapers during the holidays. The table show the number of employees who delivered papers each week and the time needed for delivery.
Number of Employees / 2 / 4 / 10 / 20Time in Minutes / 100 / 50 / 20 / 10
a. What function models this problem?
b. How many employees should there be to deliver newspapers in at most 40 minutes each week?
8-2 The Reciprocal Function Family
23.A mystery society is renting a Victorian mansion for a murder mystery party. The owner is charging the group, which has 75 members, $650 for the weekend rental but does not want more than 30 people in the house. All of the members attending the party will split the cost of the rental equally except that the member playing the dead body does not have to pay. Model the cost per member Cas a function of the number of members attending n. How many members have to attend for the cost to be less than $25 per person?
24. The junior class is buying keepsakes for Class Night. The price of each keepsake p is inversely proportional to the number of keepsakes sbought. The keepsake company also offers 10 free keepsakes in addition to the class’s order. The equation models this inverse variation.
a. If the class buys 240 keepsakes, what is the price for each one?
b. If the class pays $5.55 for each keepsake, how many can they get, including
the free keepsakes?
8-6 Solving Rational Equations
25. You can paint a fence twice as fast as your sister can. Working together, the two of you can paint a fence in 6 h. How many hours would it take each of you working alone?
26. A passenger train travels 392 mi in the same time that it takes a freight train to travel 322 mi. If the passenger train travels 20 mi/h faster than the freight train, find the speed of each train.
27. You can travel 40 mi on your motorbike in the same time it takes your friend to travel 15 mi on his bicycle. If your friend rides his bike 20 mi/h slower than you ride your motorbike, find the speed for each bike.