Notes 1.9
Functions and their
Graphs
1. Coordinate Plane Basics
y-axis
x-axis
Origin
(0, 0)
A point,
named by an
ordered pair
(x, y)
In this case
( , )
A. Quadrants
Quadrant II
X<0, y>0
Quadrant I
X>0, y>0
Origin (0,0)
Quadrant III
X<0, y<0
Quadrant IV
X>0, y<0
B. Plotting Points
Plot the following
points:
(3, 5)
(-3, 5)
(-3, -5)
(3, -5)
II. Independent and
Dependent Variables
• In an equation, the input variable is called the
independent variable.
• The output variable is called the dependent
variable and depends on the value of the input
variable.
• In y=2x-7 ….. x is the independent variable
y is the dependent variable
• The graph of an equation in 2 variables is the
collection of all points (x,y) whose coordinates are
solutions of the equation.
Identify the independent and dependent variables for
the following situations:
• A. In general, the average price of gasoline slowly
increases and decreases throughout the year
B. Students are selling art pieces to raise money. The
more pieces they sell, the more money they make.
C. The more I drive, the more I pay for gas.
D. The amount of coffee people drink on average
varies throughout the day.
III. Graphing an equation in 2 variables
1. Construct a table of values
with enough solutions to
recognize a pattern
2. Plot the points and connect
them with a line or curve
Graph: y = x + 1
Step 1
Table of values
Step
3:
Step2:
IV. Graphing and Evaluating Functions
• Many functions can be represented by an
equation in 2 variables: y=2x-7
• An ordered pair is a solution if the equation is
true when the values of x & y are substituted
into the equation.
• Ex: (2,-3) is a solution of y=2x-7 because:
• -3 = 2(2) – 7
• -3 = 4 – 7
• -3 = -3
Ex 1: Determine if the
following are
solutions to y = 2x - 5
a) (3, 1)
b) (1, -2)
Ex. 2: Determine if the
following points are on
the graph of y = -3x - 5
a) (-1, -2)
b) (5, 10)
V. Discrete vs Continuous
A. Discrete
• The graph consists of separate points, and
it makes no sense to connect the points in
this situation.
Discrete Example
• How much I could pay for $100 basketball
shoes depending on how many pairs I buy?
• How many dogs that have been adopted from
the animal shelter throughout the year?
• How many students in BNHS as the year goes
on?
B. Continuous
• The graph is an unbroken line or curve. It
makes sense to connect the points in this
situation.
Continuous Example
• The miles a car travels from home over
time.
• The amount of water in a bathtub with
the faucet on.
VI: Analyzing Functions
You Try: Journal Time!
• What are the three graphs describing?
• What is happening in Graph A? B? C?