Algebra AUnit 5 Introduction to Functions Review1

Name ______Class period ______

Functions

#1 and #2 For each table, determine whether the relationship is a function. Then represent the relationship using words, an equation, and a graph.

#1

#2

#3 and #4 Graph the function shown by each table. Tell whether the function is linear or nonlinear. Explain your answer.

#3

#4

#5Writing. How can you determine if a function is linear or nonlinear from the graph of the function?

#6Error Analysis. A student says that the function shown by the table below can be represented by the

rule y = x2 – 1. Describe and correct the error.

#7 through #10 Make a table of values for each function. Then graph the function rule.

#7 #8

x / -2 / -1 / 0 / 1 / 2
y
x / -2 / -1 / 0 / 1 / 2
y

#9 #10

x / y
-3
-2
-1
0
1
2
3
x / y
-3
-2
-1
0
1
2
3

Identify the domain and range of each relation. Use a mapping diagram to determine whether the relation is a function. Explain how you determined if the relation is a function.

#11{(2,4), (8,11), (9,1), (4,2)}#12{(6, 5), (5, 6), (2, 2), (2, 6)}

Use the vertical line test to determine whether the relation is a function. Explain how the vertical line test works.

#13

Given and , calculate each of the following. Show your work.

#14 f(-2)#15 f(0)#16g(3)#17g(-1)

#18f(7)#19f()#20g(0.25)#21g(0)

What are the variables in each graph? Identify the independent and dependent variables. Describe how the variables are related at various points on the graph.

#22#23

#24Which graph shown below represents the information in the table? Explain your answer.

#25 and #26Sketch a graph to represent each situation. Label each section. Define and identify the independent and dependent variables.

#25The price of gasoline has steadily increased over the last 10 years.

#26The level of water in a river rose rapidly during the storm and the gradually decreased back to the

original level.

#27 A worker’s wages W, in dollars, is a function of the number of hhours worked. Graph the function shown by the table. Tell whether the function is linear or nonlinear. Explain your answer.

#28 and #29 Make a table of values and graph each function rule. Explain your choice of intervals on the axes of the graph. Tell whether the graph is continuous or discrete.

#28 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.

w
d

#29 The price p, in dollars, for apples depends on the weight w, in pounds, of apples. This situation is represented by the function rule p=1.99w.

w / p

#30 and #31 Write a function rule that represents each situation.

#30The price pof a large cheese pizza is $7.95 plus $0.75 for each topping t on the pizza.

#31Eric’s earnings mare a function of the number of lawns n he mows at a rate of $12 per lawn.

#32An online music club charges $5.75 for the first music download and $2 for each additional download

per month. Write a rule describing the total monthly fees f as a function of additional downloads d.

What are the fees for 15 music downloads in a month? Show your work

#33Write a function rule for the area of a rectangle whose length is 6 ft more than its width. What is the

area of the rectangle when its width is 12 ft? Define the variables and show your work.

#34A tenth grade class is selling granola bars for a fundraiser. They earn $0.75 for every granola bar that

they sell. They have ordered 300 granola bars for the sale. The function represents

the profit P(b) the class earns for each bar b they sell. Describe a reasonable domain and range for

the function.