Download Chapter 4 Note Packet

Algebra I Chapter 4 Section 1 Graphing Relationships
Warm up
State whether each word or phrase represents an amount that is increasing, decreasing, or constant.
1.
Stays the same
2. Rises
3. Drops
4. Slows down
Key Words
Was constant
Rose steadily
Stayed the same
Dropped sharply
Segment Description
Graphs
Which graph best represents the following situation?
The air temperature increased steadily for several hours and then remained constant. At the end of the
day, the temperature increased slightly again before dropping sharply. Choose the graph that best
represents this situation.
Some graphs are connected line or curves called _____________ graphs. Some graphs are only distinct
points. These are called ____________ graphs.
Sketch a graph for each situation. Tell whether the graph is continuous or discrete.
Jamie is taking an 8-week keyboarding class. At the end of each week, she takes a test to find the
number of words she can type per minute. She improves each week.
Henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the
first valve. He leaves the second valve open until the tank is empty.
Each day several leaves fall from a tree. One day a gust of wind blows off many leaves. Eventually there
are no more leaves on the tree. Choose the graph that best represents this situation.
Graph A
Graph B
Graph C
Sketch a graph for each situation. Tell whether the graph is continuous or discrete.
A truck driver enters a street, drives at a constant speed, stops at a light and then continuous
A small bookstore sold between 5 and 8 books each day for 7 days
Write a possible situation for the given plot
Homework 4-1 pg 233 #10-19, 23-25, 29-37
Algebra I chapter 4 section 2 Relations and Functions
Warm up
Generate ordered pairs for the function y = x + 3 for x = -2, -1, 0, 1, and 2. Graph the ordered pairs
Relationships can also be represented by a set of ordered pairs called a _____________
In the scoring system of some track meets, for first place you get 5 points, for second place you get 3
points, for third place you get 2 points, and for fourth place you get 1 point. This scoring system can be
shown as ordered pair, {(1,5), (2,4), (3,2), (4,1)} You can also show relations in other ways, such as
tables, graphs or _________________ diagrams.
Express the scoring system as a table, as a graph, and as a mapping diagram.
The ______________ of a relation is the set of first coordinates (or __ values) of the ordered pairs.
The _________ of a relation is the set of second coordinates (or ___ values) of the ordered pairs.
Give the domain and range of {(1,5), (2,4), (3,2), (4,1)}
Give the domain and range of each relation.
X
1
4
8
Y
1
4
1
A ________________________ is a special type of relation that pairs each domain value with exactly
one range value.
Give the domain and range of each relation. Tell whether the relation is a function.
X
3
5
4
3
Y
-2
-1
0
1
{(8,2),(-4,1),(-6,2),(1,9)}
Homework 4-2 pg 239 #15-20, 24-25, 32-35, 39-42
Algebra I chapter 4 section 2 Vertical Line Test
Use the vertical line test to determine if the following graphs are functions
Homework worksheets
Algebra I Chapter 4 Section 3 writing functions
Warm-up
Evaluate each expression for a = 2, b = -3 and c = 8
a + 3c
ab – c
½c+b
4c – b
ba + c
Determine a relationship between the x and y values. Write an equation
x
y
1
-2
2
-1
3
0
4
1
15
3
20
4
{(1,3), (2,6), (3,9), (4,12)}
x
y
5
1
10
2
The input of a function is the ____________________ variable. The output of a function is the
_________________ variable. The value of the dependent variable depends on the value of the
independent variable.
The amount of money you make depends on the amount of hours you work.
Independent ______________
Dependent ________________
Identify the independent and dependent variables in each situation.
A painter must measure a room before deciding how much paint to buy.
The height of a candle decreases d centimeters for every hour it burns.
A veterinarian must weigh an animal before determining the amount of medication.
A company charges $10 per hour to rent a jackhammer.
Camryn buys p pounds of apples at $0.99 per pound.
An algebraic expression that defines a function is a _______________________.
If x is the independent variable and y is the dependent variable, then _____________________ for y
is f(x), read “__________”
There are several different ways to describe the variables of a function.
Independent variable
Dependent variable
Identify the independent and dependent variable. Write a rule in function notation for each situation.
A lawyer’s fee is $200 per hour for her services.
Steven buys lettuce that costs $1.00 per lb.
A math tutor charges $35 per hour.
A fitness center charges a $100 initiation fee plus $40
Evaluate each function for the given input values.
f(x) = 3x + 2, find f(x) when x = 7 and when x = -4
g(t) = 1.5t – 5, find g(t) when t = 6 and when t = -2
h(r) = 1/3r + 2, find h(r) when r = 600 and when r = -12
Joe has enough money to purchase 1, 2, or 3 DVDs at $15.00 each. Write a function to describe the
situation. Find a reasonable domain and range for the function.
The settings on a space heater are the whole numbers from 0 to 3. The total number of watts used for
each setting is 500 times the setting number. Write a function rule to describe the number of watts
used for each setting. Find a reasonable domain and range for the function.
Manuel has already sold $20 worth of tickets to the school play. He has 4 tickets left to sell at $2.50
per ticket. Write a function rule to describe how much money Manuel can collect from selling tickets.
Find a reasonable domain and range for the function.
Homework 4-3 pg 249 #13-28, 33, 34, 38-44 even
Algebra I Chapter 4 Section 4 graphing functions
Solve each equation for y
2x + y = 3
-x + 3y = -6
Generate ordered pairs for y = ½ x + 1 using x = -4, -2, 0, 2, and 4
Graph each function for the given domain
-x + 2y = 6: D = {-4, -2, 0, 2}
4x – 2y = 8
Graph each function for the given domain
x– 3y - -6: D = {-3, 0, 3, 6}
f (x) = x2 – 3: D = {-2, -1, 0, 1, 2}
Graphing functions using a domain of all real numbers
Step 1
Step 2
Use the function to generate ordered pairs by choosing
several values for x
Plot enough points to see a pattern for the graph
Step 3
Connect the points with a line or smooth curve.
Graph each function.
-3x + 2 = y
f(x) = 3x – 2
𝑦 = |𝑥 − 1|
𝑔(𝑥) = |𝑥| + 2
Graph y = 1/3x + 2. Then use the graph to find the value of x when f(x) = 3
Use a graph of the function f(x) = -1/2x + 4 to find the value of f(x) when x = -4.
Graph y = x2
A mouse can run 3.5 meters per second. The function y = 3.5x describes the distance in meters the
mouse can run in x seconds. Graph the function. Use the graph to estimate how many meters a mouse
can run in 2.5 seconds.
Homework 4-4 pg 256 #13-26, 28-36 even, 37-40, 48-52 even, 58-61
Algebra I Chapter 4 section 4 Connect function rules, tables and graph
Technology Lab
Homework worksheet
Algebra I chapter 4 Section 5 Scatter plots and trend lines
Graph each point
A(3,2)
B(-3,3)
C(-2,-1)
D(0,-3)
E(1,0)
F(3,-2)
A _______________ is a graph with points plotted to show a possible relationship between two set of
data.
The table shows the number of points scored by a high school football team in the first four games of a
season. Graph a scatter plot using the given data points.
Game
score
1
6
2
21
3
46
4
34
The table shows the number of cookies in a jar from the time since they were baked. Graph a scatter
plot using the given data.
COOKIES IN THE JAR
TIME SINCE
BAKED
COOKIES
1
2
3
4
24
16
10
7
A ____________ DESCRIBES A RELATIONSHIP BETWEEN TWO DATA SETS. The correlation can
help you analyze trends and make predictions. There are three types of correlations between data.
Identify the correlation you would expect to see between each pair of data sets.
The number of hours watching TV and your test score
The average temperature and the number of visitors at the beach
The number of empty seats in a classroom and the number of students seated in the class
The number of people in an audience and ticket sales
The average temperature in a city and the number of tickets given in the city
A runner’s time and the distance to the finish line
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs.
Choose the scatter plot that best represents the relationship between the number of minutes since a pie
has been taken out of the oven and the temperature of the pie.
Homework 4-5 pg 266 #14-24, 29-30, 34-41
Algebra I chapter 4 Section 5
Interpret scatter plots and trend lines
Homework worksheet
Algebra I Chapter 4 Section 6 Arithmetic Sequences
Warm up
Evaluate
5 + (-7)
5.3 + 0.8
-3(2-5)
6(4 – 1)
n – 2.8 where n = 5.1
6(x-1) where x = 5
A _______________ is a list of numbers that often forms a pattern. Each number in a sequence is a
__________.
When the terms of a sequence differ by the same nonzero number d, the sequence is an
_____________ sequence and d is the ________________ difference.
Determine whether each sequence appears to be an arithmetic sequence. If so, find the common
difference and the next three terms.
9, 13, 17, 21, …
12, 8, 4, 0, …
1, 4, 9, 16, …
10, 8, 5, 1, …
Finding the nth term of an arithmetic sequence
The nth term of an arithmetic sequence with common difference d and first term a1 is
an = a1 + (n – 1)d
Find the indicated term of each arithmetic sequence.
16th term 4, 8, 12, 16, …
22nd term 5, 2, -1, -4, …
25th term a1 = -5; d = -2
12th term a1 = 4.2; d = 1.4
Each time a truck stops, it drops off 250 pounds of cargo. It started with a load of 2000 pounds. How
much does the load weigh after the fifth stop?
A bag of cat food weighs 18 pounds. Each day, the cats are fed 0.5 pound of food. How much does the
bas of cat food weigh after 30 days?
Homework 4-6 pg 275 #10-14 even, 16-30 even, 34-37, 42-44, 48-54 even