Download Slide 1

Review
Chapter 4 Sections 1-6
The Coordinate
Plane
4-1
Vocabulary
Axes
Origin
Coordinate plane
Y-axis
X-axes
X-coordinate
Y-coordinate
Quadrant
Graph
The Coordinate Plane
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5
Axes – two perpendicular number
lines.
y
Origin – where the axes intersect
at their zero points.
1 2 3 4 5
x
Origin
(0,0)
X-axes – The horizontal number
line.
Y-axis – The vertical number line.
Coordinate plane – the plane
containing the x and y axes.
Quadrants
II
(–,+)
5
4
3
2
1
-5 -4 -3 -2 -1
-1
-2
-3
(–, –) -4
-5
III
y
I
(+,+)
1 2 3 4 5
IV
(+, –)
x
Quadrants – the x-axis and yaxis separate the coordinate
plane into four regions.
Notice which quadrants contain
positive and negative x and y
coordinates.
Coordinates
5
4
3
2
(0, 0) 1
-5 -4 -3 -2 -1
-1
-2
origin -3
-4
-5
y
To plot an ordered pair, begin at the
origin, the point (0, 0), which is the
intersection of the x-axis and the y-axis.
(2, 3)
1 2 3 4 5
x
The first coordinate tells how many units to
move left or right; the second coordinate
tells how many units to move up or down.
move right
2 units
(2, 3)
x-coordinate move
right or left
move up
3 units
y-coordinate move
up or down
To graph an ordered pair means to draw a dot at the
point on the coordinate plane that corresponds to the
ordered pair.
Transformations on
the Coordinate
Plane
4-2
Vocabulary







Transformation – movements of geometric figures
Preimage – the position of the figure before the
transformation
Image – the position of the figure after the transformation.
Reflection – a figure is flipped over a line (like holding a
mirror on it’s edge against something)
Translation – a figure is slid in any direction (like moving a
checker on a checkerboard)
Dilation – a figure is enlarged or reduced.
Rotation – a figure is turned about a point.
Types of Transformations
Reflection and Translation
Dilation and Rotation
Relations
4-3
Vocabulary



Mapping – a relation represented by a set
of ordered pairs.
Inverse – obtained by switching the
coordinates in each ordered pair. (a,b)
becomes (b,a)
Relation – a set of ordered pairs
Mapping, Graphing, and Tables
Mapping the Inverse
Equations as
Relations
4.4
Vocabulary


Equation in two variables – an equation
that has two variables
Solution – in the context of an equation with
two variables, an ordered pair that results
in a true statement when substituted into
the equation.
Different Ways to Solve


Solving using a replacement set – a variation of
guess and check. You start with an equation and
several ordered pairs. You plug each ordered pair
into the equation to determine which ones are
solutions.
Solving Using a Given Domain – Start with an
equation and a set of numbers for one variable
only. You then substitute each number in for the
variable it replaces, and solve for the unknown
variable. This gives you a set of ordered pairs
that are solutions.
Dependent Variables
When you solve an equation for one variable, the
variable you solve for becomes a “Dependent
Variable”. It depends on the values of the other
variable.
3x  5  y
Independent
Variable
Dependent
Variable
The values of “y” depend on
what the value of “x” is.
Graphing Linear
Equations
4.5
Vocabulary




Linear equation – the equation of a line
Standard form – Ax + By = C where A, B, and C
are integers whose greatest common factor is 1, A
is greater than or equal to 0, and A and B are both
not zero.
X-intercept – The X coordinate of the point at
which the line crosses the x-axis (Y is equal to 0)
Y-intercept – the Y coordinate of the point at
which the line crosses the y-axis (X is equal to 0)
Methods of Graphing

Make a table –





Solve the equation for y.
Pick at least 3 values for x and solve the equation for the 3
values of y that make the equation true.
Graph the resulting x and y (ordered pair) on a coordinate
plane.
Draw a line that includes all points.
Use the Intercepts –






Make X equal to zero.
Solve for Y.
Make Y equal to zero.
Solve for X.
Graph the two coordinate pairs: (0,Y) and (X,0)
Draw a line that includes both points.
Functions
4.6
Vocabulary



Function – a relation in which each element of the
domain is paired with exactly one element of the
range (for each value of x there is a value for y,
but each value of y cannot have more than one
value of x)
Vertical line test – if no vertical line can be drawn
so that it intersects the graph in more than one
place, the graph is a function
Function notation – f(x) replaces y in the equation.
Vertical Line Test
Function Notation
f(5)
=3(5)-8
=15-8
=7
Other Functions and Notations


Non-Linear Functions – Functions that do
not result in a line when plotted.
Alternative Function Notation – another
way of stating f(x) is <<x>>.