review chapter 4 sections 1-6. the coordinate plane 4-1
TRANSCRIPT
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ReviewChapter 4 Sections 1-6
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The Coordinate Plane
4-1
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Vocabulary
AxesOrigin
Coordinate planeY-axisX-axes
X-coordinateY-coordinate
QuadrantGraph
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The Coordinate Plane
x
y
Axes – two perpendicular number lines.
Origin – where the axes intersect at their zero points.
X-axes – The horizontal number line.
Y-axis – The vertical number line.
Coordinate plane – the plane containing the x and y axes.
1 2 3 4 5-1-2-3-4-5
12345
-1-2-3-4-5
Origin (0,0)
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Quadrants
x
y
1 2 3 4 5-1-2-3-4-5
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-1-2-3-4-5
III
III IV
Quadrants – the x-axis and y-axis separate the coordinate plane into four regions.
Notice which quadrants contain positive and negative x and y coordinates.
(+,+)(–,+)
(–, –) (+, –)
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Coordinates
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.
x
y
1 2 3 4 5-1-2-3-4-5
12345
-1-2-3-4-5
The first coordinate tells how many units to move left or right; the second coordinate tells how many units to move up or down.
(2, 3)origin
move right 2 units
move up 3 units
(0, 0)
(2, 3)
To graph an ordered pair means to draw a dot at the point on the coordinate plane that corresponds to the
ordered pair.
x-coordinate move right or left
y-coordinate move up or down
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Transformations on the Coordinate
Plane4-2
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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.
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Types of Transformations
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Reflection and Translation
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Dilation and Rotation
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Relations4-3
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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
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Mapping, Graphing, and Tables
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Mapping the Inverse
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Equations as Relations
4.4
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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.
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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.
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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.
yx 53Dependent Variable
Independent Variable
The values of “y” depend on what the value of “x” is.
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Graphing Linear Equations
4.5
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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)
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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.
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Functions4.6
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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.
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Vertical Line Test
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Function Notation
f(5) =3(5)-8
=15-8
=7
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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>>.