8-1 Relations and Functions PRE-ALGEBRA LESSON 8-1 Determine if and where Will and Pedro will meet if they start driving from the same intersection. Pedro travels 2 blocks east, 2 blocks south, 2 blocks east, and 2 blocks north. Will starts traveling 2 blocks north, 4 blocks east, and 2 blocks south. Yes, they will meet 4 blocks east.
72
Embed
8-1 Relations and Functions PRE-ALGEBRA LESSON 8-1 Determine if and where Will and Pedro will meet if they start driving from the same intersection. Pedro.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Determine if and where Will and Pedro will meet if they startdriving from the same intersection. Pedro travels 2 blocks east, 2blocks south, 2 blocks east, and 2 blocks north. Will starts traveling2 blocks north, 4 blocks east, and 2 blocks south.
Yes, they will meet 4 blocks east.
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Graph each point.
1. A(3, 4) 2. B(–3, 1) 3. F(2, 0)
4. D(2, –2) 5. C(–4, –3) 6. E(0, –4)
(For help, go to Lesson 1-10.)
Check Skills You’ll Need
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Solutions
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Is each relation a function? Explain.
a. {(0, 5), (1, 6), (2, 4), (3, 7)}
List the domain values and the range values in order.
Draw arrows from the domain values to their range values.
There is one range value for each domain value. This relation is a function.
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
(continued)
b. {(0, 5), (1, 5), (2, 6), (3, 7)}
There is one range value for each domain value. This relation is a function.
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
(continued)
c. {(0, 5), (0, 6), (1, 6), (2, 7)}
There are two range values for the domain value 0.
This relation is not a function.
Quick Check
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Is the time needed to mow a lawn a function of the
size of the lawn? Explain.
No; two lawns of the same size (domain value) can require different lengths of time (range values) for mowing.
Quick Check
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
a. Graph the relation shown in the table.
Domain Value
–3
–5
3
5
Range Value
5
3
5
3
Graph the ordered pairs(–3, 5), (–5, 3), (3, 5), and (5, 3).
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
b. Use the vertical-line test. Is the relation a function? Explain.
(continued)
The pencil does not pass through two points at any one of its positions, so the relation is a function.
Pass a pencil across the graph as shown. Keep the pencil vertical (parallel to the y-axis) to represent a vertical line.
Quick Check
8-1
Relations and FunctionsRelations and FunctionsPRE-ALGEBRA LESSON 8-1PRE-ALGEBRA LESSON 8-1
Is each relation a function? Explain.
1. {(–2, –1), (4, 2), (–8, –4), (6, 3)}
2. {(5, 0), (7, 2), (9, 4), (5, 1)}
3. Graph the relation in the table.
Is the relation a function?
Explain.
x
y
–1
7
0
7
1
7
2
7
Yes; there is only one range value for each domain value.
No; the domain value 5 has two range values, 0 and 1.
Yes; there is one range value for each domain value. Check students’ graphs.
8-1
8-2
Equations With Two VariablesEquations With Two VariablesPRE-ALGEBRA LESSON 8-2PRE-ALGEBRA LESSON 8-2
Identify the data needed: At a fundraiser, $5 was collected fromeach parent and $1 was collected from each child. How muchmoney was raised?
the number of parents and children at the fundraiser
PRE-ALGEBRA LESSON 8-2PRE-ALGEBRA LESSON 8-2
Evaluate each expression for x = 2.
1. 2 + x 2. x – 12 3. 8x – 13 4. 24 ÷ 2x
(For help, go to Lesson 1-3.)
Check Skills You’ll Need
8-2
Equations With Two VariablesEquations With Two Variables
a. Describe the person represented by the point with coordinates (10, 30).This person has 10 years of education and earns $30,000 each year.
b. How many people have exactly 14 years of education? What are their incomes?The points (14, 50), (14, 80), and (14, 90) have education coordinate 14.The three people they represent earn $50,000, $80,000, and $90,000, respectively.
Answer the following questions based on the graph.
1. What do you know about the student at point A?
2. How many students read 3 books per month?
3. Is there a positive correlation, a negative correlation, or no correlation between books read and semester grades?
read 2 books per month, grade: 80
positive correlation
3
8-5
8-6
Problem Solving Strategy: Solve by GraphingProblem Solving Strategy: Solve by GraphingPRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
Draw 6 nonlinear points. How many different segments can you draw connecting two points?
15
Problem Solving Strategy: Solve by GraphingProblem Solving Strategy: Solve by GraphingPRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
Write a rule for each linear function.
1. 2.
(For help, go to Lesson 8-4.)
8-6
Check Skills You’ll Need
Problem Solving Strategy: Solve by Graphing Problem Solving Strategy: Solve by Graphing PRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
Solutions
1. slope = = = 2
y-intercept = 2
A rule for the function is f(x) = 2x + 2.
2. slope = = = –
y-intercept = –3
A rule for the function is f(x) = – x – 3.
6 – 22 – 0
42
–2 – (– 3)–4 – 0
1–4
14
14
8-6
Problem Solving Strategy: Solve by Graphing Problem Solving Strategy: Solve by Graphing PRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
Use the data in the table below. Suppose this year
there are 16 wolves on the island. Predict how many moose
are on the island.
Isle Royale Populations
Wolf Moose
14
23
24
22
20
16
700
900
811
1,062
1,025
1,380
Year
1982
1983
1984
1985
1986
1987
Wolf Moose
12
11
15
12
12
13
1,653
1,397
1,216
1,313
1,600
1,880
Year
1988
1989
1990
1991
1992
1993
Wolf Moose
15
16
22
24
14
25
1,800
2,400
1,200
500
700
750
Year
1994
1995
1996
1997
1998
1999
8-6
Step 1 Make a scatter plot by graphing the (wolf, moose) ordered pairs. Use the x-axis for wolves and the y-axis for moose.
Step 2 Sketch a trend line. The line should be as close as possible to each data point. There should be about as many points above the trend line as below it.
Problem Solving Strategy: Solve by Graphing Problem Solving Strategy: Solve by Graphing PRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
(continued)
8-6
Look up to find the point on the trend line that corresponds to 16 wolves.
Then look across to the value on the vertical axis, which is about 1,300.
Problem Solving Strategy: Solve by Graphing Problem Solving Strategy: Solve by Graphing PRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
(continued)
Step 3 To predict the number of moose when there are 16 wolves, find 16 along the horizontal axis.
There are about 1,300 moose on the island.
Quick Check
8-6
Problem Solving Strategy: Solve by Graphing Problem Solving Strategy: Solve by Graphing PRE-ALGEBRA LESSON 8-6PRE-ALGEBRA LESSON 8-6
Answer each question.
1. When is there no trend line for a scatter plot?
2. What type of correlation will the data have for a scatter plot of ages and heights of all students in your school?
3. Why is it important to say “about” when making a prediction?
when there is no correlation
The prediction is based on a trend line that approximates the locations of the related points.
positive
8-6
8-7
Solving Systems of Linear EquationsSolving Systems of Linear EquationsPRE-ALGEBRA LESSON 8-7PRE-ALGEBRA LESSON 8-7
Find the slope and y-intercept for the equation 1.3x – y + 5 = 0.
Slope is 1.3; y-intercept is 5.
Solving Systems of Linear EquationsSolving Systems of Linear EquationsPRE-ALGEBRA LESSON 8-7PRE-ALGEBRA LESSON 8-7