Transcript Ch 1-8 Graphs and Functions

Graphs and Functions
1. Identify the hypothesis and the conclusion and write the
statement in if-then form.
2
When x  x  7  9, x  2
If x 2  x  7  9 , then x  2 .
Hypothesis
Conclusion
2. Which number is a counterexample for x  x 3
A. – 5
B. 0
C. 2
D. – 1
?
Graphs and Functions
A function is a relationship between input and
output.
In a function, the output depends on the input.
There is exactly one output for each input.
y
The vertical
number line is
called the y-axis.
6
The coordinate system is
also called the
coordinate plane.
5
4
3
2
1
9
8 7 6 5 4 3 2 1 0
1
1
2
3
4
5
6
7
8
2
The origin is at (0, 0),
the point at which the
number lines intersect.
3
4
5
6
The horizontal
number line is
called the x-axis.
9
x
Graphs and Functions
An ordered pair of numbers is used to locate
any point on a coordinate plane.
The first number is called the x-coordinate.
The second number is called the y-coordinate.
(3, 2)
The x-coordinate
corresponds to a
number on the x-axis.
The y-coordinate
corresponds to a
number on the y-axis.
Copy the ordered pair and labels into your notes.
Identify Coordinates
Sports Medicine Name the ordered pair at point E and
explain what it represents.
Answer: Point E is at 6
along the x-axis and 100
along the y-axis. So, its
ordered pair is (6, 100). This
represents 100% normal
blood flow 6 days after the
injury.
Identify Coordinates
Name the ordered pair at point D and explain
what it represents.
Answer: (4, 97)
This represents 97% normal
blood flow 4 days after the
injury.
Graphs and Functions
In this example, the percent of normal blood flow
depends on the number of days from injury.
Therefore, the number of days from injury is called
the independent variable or quantity and the percent
of normal blood flow is called the dependent
variable.
TITLE
y
y-axis label
dependent variable
Graphs and Functions
36
32
28
24
20
16
12
8
4
0
1 2
3 4 5 6 7 8
9 x
x-axis label
independent variable
Copy this into your notes.
Independent and Dependent Variables
Energy In warm climates, the average amount of
electricity used in homes each month rises as the
daily average temperature increases, and falls as
the daily average temperature decreases. Identify
the independent and the dependent variables for
this function.
Answer: Temperature is the independent variable as it is
unaffected by the amount of electricity used. Electricity
usage is the dependent variable as it is affected by the
temperature.
Independent and Dependent Variables
In a particular club, as membership dues
increase, the number of new members
decreases. Identify the independent and
dependent variable in this function.
Answer: Membership dues is the independent variable.
Number of new members is the dependent
variable.
Graphs and Functions
Functions can be graphed without using a scale on
either axis to show the general shape of the graph
that represents a function.
Analyze Graphs
The graph represents the temperature in Ms. Ling’s
classroom on a winter school day. Describe what is
happening in the graph.
Sample answer: The temperature is low until the heat is
turned on. Then the temperature fluctuates up and down
because of the thermostat. Finally the temperature drops
when the heat is turned off.
Analyze Graphs
The graph below represents Macy’s speed as she
swims laps in a pool. Describe what is happening
in the graph.
Sample answer: Macy’s speed increases as she crosses
the length of the pool, but then stops when she turns
around at the end of each lap.