CORNELL NOTES
Name _______________________
SOL:
Date ____________
Standard A.7
The student will investigate and analyze function (linear and quadratic) families and their
characteristics both algebraically and graphically, including a)determining whether a relation is
a function; b)domain and range; c)zeros of a function; d)x- and y-intercepts;
TOPIC: Plotting points and drawing lines on a coordinate plane.
Content and Language
Objectives
Day 1: Create a coordinate plane and label its parts. Plot points in the correct (x,y)
form. Connect points to draw a line. Identify the quadrants in a coordinate plane.
Day 2: Define relation. Define function. Graph a linear equation. Recognize the domain
and the range from a function table, a map, coordinate points, and a graph
accordingly.
Day 3: Identify x– and y– intercepts of a graphed function. Find the zeros of a function.
Vocabulary
two-dimensional
What is a coordinate plane?
plot
The coordinate plane is a ____________________ surface on which we
can___________ points, lines and curves.
How many right angles
does a coordinate
plane have?
______________
Draw:
a Point
a Line
a Curve
x-axis
y-axis
It has two scales, called the _____________ and _____________, at right
angles to each other.
The plural of axis is
'axes'.
Draw angles:
Points on the plane
are located using
two numbers - the x
and y coordinates.
These are the
horizontal and
vertical distances of
the point from a
specific location
called the origin.
The center
(0,0)
acute angle
obtuse angle
straight angle
right angle
Origin
Where is the ORIGIN? ___________
Ordered pair for ORIGIN: _______
X axis
horizontal scale
The _________________________ is called the x-axis. As you go to the right on
the scale from zero, the values are positive and get larger. As you go to the left
from zero, they get more and more negative.
vertical scale
Y axis
The ________________________ is called the y-axis. As you go up from zero
the numbers are increasing in a positive direction. As you go down from zero
they get more and more negative.
Ordered pairs are
written in this form:
(X,Y)
Quadrants
The two axes divide the plane into four areas called
quadrants
___________________. The first quadrant is the top right, and then
they go around counter-clockwise.
They are sometimes labeled with Roman numerals: I, II, III and IV.
counter-clockwise:
(3,2)
REMEMBER
The coordinates of the origin are (0, 0). The first number in an ordered pair is
X
Y
the x-coordinate. The second number is the y-coordinate. The numbers in an
ordered pair are called coordinates.
In which quadrant can
you find the following
points?
(4, 6) _____________
(-4, 6)_____________
(-4, -6)____________
(4, -6)_____________
Functions
rule
A function is a ___________ that associates one and only one ______________ of one
value
variable with each value of another variable.
The function y
= 2x expresses y in terms of x. For each value of x, there is one and
only one value of y.
An equation determines y as a function of x, if for each x, the equation can be solved
lines
to give exactly one value of y.
linear equation
The graphs of such equations are________________ in the plane.
An equation that can be written Ax + By = C, where A, B, and C are fixed numbers, is
called a __________________________.
table of values
The graph of a linear equation is a straight line.
To graph a linear equation, first a _______________________________ for x and y is
completed and then the ordered pairs are graphed.
Finally a line is drawn through the points.
FUNCTION?
___________
Equation: y = x + 3
This is a _________________________________
These values can be interpreted as the x-coordinates and y-coordinates of points in
the coordinate plane. Graphing these points means placing a dot at the points (–2, +1),
(–1, +2), (0, +3), (+1, +4), and (+2, +5). To graph the equation, students connect the
points with a straight line.
FUNCTION -OR- RELATION
What is a relation?____________________________________________
What is a function?____________________________________________
An connection) of members of the domain (x) with exactly ONE
MAPPING
Example: A.
Example: B.
9
12
6
0
21
5
6
0
8
12
21
10
0
3
6
6
1
Ex. A. is a ___________________
Ex. B. is a ___________________
Why? _________________________________________________________Example
A has each “x” associated (co
)CO-ORDINATE POINTS
Use the mapping above to make co-ordinate points:
(
Ex. A.
(
,
)
,
)
(
(
,
) (
,
,
)
)
Ex. A. is a ___________________
Ex. B.
(
,
(
)
,
(
)
,
(
)
(
,
,
)
)
Ex. B. is a ___________________
Why?______________________________________________________________
In Example A no x is repeated. In Example B the “x” repeats BUT the “y”
GRAPHING
4
4
3
3
2
2
1
1
Ex. A.
Ex. B.
-4
-3
-2
-1
1
2
3
4
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
Ex. A. is a ___________________
2
3
4
Ex. B. is a ___________________
Why?
_______________________________________________________________values.
This fails t
DOMAIN & RANGE
X values
What is Domain? ___________________________________________________
What is Range? ____________________________________________________
Y values
input
_____________Example A no x is repeated. In Example B the “x” repeats BUT the “y”
4
4
for each
is d
output
-4
-3
-2
D: {
R: {
3
3
2
2
1
1
-1
1
2
3
4
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
}
}
D: {
R: {
2
3
4
}
}
_______________________________________________________________________
9
12
0
6
12
21
5
21
6
0
10
0
8
6
3
6
1
D: {
R: {
}
}
D: {
R: {
}
}
_________________________________________________________________
Again, use the above mapping to make your coordinate points.
(
,
)(
(
,
,
)(
,
) (
,
)
)
(
,
) (
(
,
,
) (
) (
,
,
)
)
IDENTIFY THE x – and y – INTERCEPTS from GRAPHED Functions
What is intercept?
_________________
x– intercept _______
x– intercept ______
x– intercept ______
y– intercept _______
y– intercept ______
y– intercept ______
FIND the ZEROS of a FUNCTION
The ZEROS of a function are the same thing as the _______________________.
1.
2.
zeros: ________________
3.
zeros: ____________
4.
zeros: ________________
5.
zeros: ________________
zeros: ____________
6.
zeros: ____________
1.