review chapter 4 sections 1-6. the coordinate plane 4-1
TRANSCRIPT
ReviewChapter 4 Sections 1-6
The Coordinate Plane
4-1
Vocabulary
AxesOrigin
Coordinate planeY-axisX-axes
X-coordinateY-coordinate
QuadrantGraph
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.
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Origin (0,0)
Quadrants
x
y
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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.
(+,+)(–,+)
(–, –) (+, –)
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
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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
Transformations on the Coordinate
Plane4-2
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
Relations4-3
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.
yx 53Dependent Variable
Independent 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.
Functions4.6
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>>.