Sect 4.1, 4.2, 4.4, 4.5, 4.6 Review
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Section 4.1 Using Graphs to Relate Two Quantities
1. Identify the independent and dependent variables. Describe how the variables are related at various points on the graph.
2. Sketch a graph of your speed as you travel on a ski lift from the bottom of a ski slope to the top.
3. Sketch a graph of your speed as you ski from the top of a ski slope to the bottom.
4. Are the graphs for problems 2 and 3 the same? Explain.
Section 4.2 Patterns and Linear Functions
5. The table shows the total amount of your grocery bill. Determine whether the relationship is a linear function. Then represent the relationship using words, an equation, and a graph.
Grocery Bill
Number of Soup Cans, x / Total Bill, y0 / $52.07
1 / $53.36
2 / $54.65
3 / $55.94
Linear?
Words:
Equation:
Graph:
6. The table shows the amount of paint left in a can. Identify the independent and dependent variables. Represent the relationship using words, an equation, and a graph.
Number of Chairs Painted, p / 0 / 1 / 2 / 3Paint Left (oz), L / 128 / 98 / 68 / 38
Independent variable:
Dependent variable:
Words:
Equation:
Graph:
Sect 4.4 Graphing a Function Rule
Make a table of values for each function. Then graph each function rule.
7. y = 5x – 28. x = 3
Graph each function rule. Explain whether the graph is continuous or discrete.
9. The cost d, in dollars, for a parking pass depends on the number of whole weeks w you purchase. This situation is represented by the function rule d = 25w.
10. The price p, in dollars, for apples depends on the weight w, in pounds, of the apples. This situation is represented by the function rule p = 1.99w.
Sect 4.5 Writing a Function Rule
11. An online music club charges $5.75 for the first music download and $2 for each additional download per month. Write a rule for describing the total monthly fees f as a function of additional downloads d. What are the fees for 15 music downloads in a month?
12. Ataxicabcharges$4.25forthefirstmileand$1.50foreachadditionalmile. Write a rule for describing the total rate r as a function of the total miles m. What is the taxi rate for 12 miles?
13. An orchestra buys music stands for $42 each with $298 in its bank account. Write a function rule that shows how the account balance depends on the number of stands bought.
Sect 4.6 Formalizing Relations and Functions
14. Identify the domain and range for {(3,2), (4, -7), (0, -1), (3, -7)}. Represent the relation with a mapping diagram. Is the relation a function? Explain your answer.
15. Does the graph represent a function? Why or why not?
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18. Use the following functions f(x) = 3x – 4; g(x) = x2 + 2; h(x) = 12 – 2x to find the following.
a. f(6) b. g(-4) c. g(h(7)d. f(g(h(5)
19. If f (x) = x2– 3 and f (a) = 46, what is the value of a? Explain.
19. A charter boat travels at a maximum rate of 25 miles per hour. Let d(x) represent the distance in miles, that the boat can travel in x hours.
a. Write a function rule representing this situation.
b. If the charter boat travels a maximum distance of 75 miles from the shore, what would be a reasonable domain and range?
c. Graph the function.
d. Is the graph discrete or continuous? Explain your answer.
20. State the domain and range, in interval notation, for the following graph.