Download - A function can be represented by a list of ordered pairs. {(-1, 2), (-2, 3), (-3, 4), (-4, 5)}
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A function can be represented by a
list of ordered pairs.
{(-1, 2), (-2, 3), (-3, 4), (-4, 5)}
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scalene triangle
A triangle with no congruent sides.
Scalene Not Scalene
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reflection A transformation that reflects, or
“flips”, a graph or figure across a line, called the line of reflection.
H'
I'
F'
G'
H
G
F
87-8 -7 6-6
-6
6
0 1
1
2
3
4
5
-1-2-3-4-5 2 3 4 5-1
-2
-3
-4
-5
I
Line of reflection
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A function can be represented by a verbal
description. Use words to describe
the functional relationship.
x y
-1 2
0 4
1 6
The y-values for a set of points are 4 more than twice the corresponding x-values.
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isosceles triangleA triangle with at least two
congruent sides.
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opposite of a number
The opposite of a number a, designated –a, is the number that is the same distance from zero as a, on the opposite side of the number line. The sum of opposites is 0.
-3 is the opposite of 3
-3 + 3 = 0
9876543210-1-2-3-4-5-6-7-8-9
-3 3
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square root A number that is multiplied
by itself to form a product is called a square root of that product.
Square root symbol:
Ex: 5 x 5 = 25, so
25 = 5
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translation• A translation is a transformation
that shifts or “slides” every point of a figure or graph the same distance in the same direction.
A'
B'
C'
D'
A
BC
D
Quad ABCD Quad A’B’C’D’
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A function can be represented by a
graph.• Graph the ordered pairs and the line that contains them.
x y
-2 -7
-1 -5
0 -3
1 -1
2 1
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domainThe set of all values of the
independent variable
or
all the x-coordinates in a function’s ordered pairs.
Ex: {(0, 1), (2, 5), (3, 6), (4, 9)}
Domain: {0, 2, 3, 4}
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dilation• A transformation
that is a proportional enlargement or reduction of a figure through a point called the center of dilation.
• Scale factor - Size of enlargement or reduction
• An enlargement has a scale factor > 1.
y
x
B'
A'
C'
C
BA
-9
-8
-7
-6
-5-4
-3
-2
-1
1
23
45
6
7
8
9
987654321-9 -8 -7 -6 -5 -4 -3 -2 -1
Triangle ABC is transformed into triangle A’B’C’ by the dilation using scale factor of 2
The origin is the center of dilation.
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rangeThe set of all values of the dependent variable
or
all the y-coordinates in a function’s ordered pairs.
Ex: {(0, 1), (2, 5), (3, 6), (4, 9)}
Range: {1, 5, 6, 9}
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A function can be represented by a
table.
x y-1 50 31 12 -1
f(x) = -2x + 3
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midpoint of a line segment
Point that lies halfway between the segment’s endpoints and divides it into two congruent parts
To find the midpoint, find the average of the coordinates of the endpoints of the line segment
y
xM(-1, 1)
B(4, -2)
A(-6, 4)
-9
-8
-7
-6
-5-4
-3
-2
-1
1
23
45
6
7
8
9
987654321-9 -8 -7 -6 -5 -4 -3 -2 -1
6 4 4 + ( 2) ,
2 2 M(-1 , 1)
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probability• Probability is a measure of how
likely an event is to occur.
• Probability of an event occurring must be from 0 to 1.
Ex: A number cube has faces numbered from 1 to 6. The probability of rolling an odd
number is 3 out of 6, or .3 1
= 6 2
3
5 1
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Simplifying expressions• Simplifying expressions uses
commutative, associative, and distributive properties to remove parentheses and combine like terms.
• Like terms in an algebraic expression can be combined.
• Remember that the expressions m2 and 1m2 are equivalent.
Simplify the expression: m2 + 5 – 5m2 – 1.
m2 + 5 – 5m2 – 1 = (1m2 – 5m2) + (5 – 1)
m2 + 5 – 5m2 – 1 = –4m2 + 4
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Prism• Three dimensional figure with two
bases that are congruent polygons and faces that are rectangular polygons, called lateral faces.
• Prisms are named by the shape of their base.
Lateral face
Base
Triangular Prism
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Net of a three-dimensional figure
• A two dimensional drawing that shows what a figure would look like when opened up and unfolded with its surfaces laid out flat.
Triangular Prism Net for Triangular Prism
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translation
H'
G'
F'
H
G
F
87-8 -7 6-6
-6
6
0 1
1
2
3
4
5
-2-3-4-5 2 3 4 5-1
-2
-3
-4
-5
A transformation that shifts or “slides” every point of a figure or graph the same distance in the same direction.
FGH is translated 5 units to the right and 3 units down to F’G’H’.
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Cylinder Three-dimensional figure
with two congruent circular bases and a curved surface
Base
Base
Curved surface
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dilation• A transformation
that is a proportional enlargement or reduction of a figure through a point called the center of dilation
• A reduction has a scale factor < 1. Triangle ABC is transformed
into triangle A’B’C’ by the dilation using scale factor of ½.
The origin is the center of dilation.y
xC'A'
B'
C
BA
-9
-8
-7
-6
-5-4
-3
-2
-1
1
23
45
6
7
8
9
987654321-9 -8 -7 -6 -5 -4 -3 -2 -1
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Cross product
• One way to solve a proportion is to use the cross product.
3=
14 22 =3 14
2x = 42
x = 21
x
x
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Rational Numbers• Numbers that can be written as the
ratio of two integers, , where b 0.
• Integers are the set of all positive and negative whole numbers, and zero.
a
b
Rational Numbers
Not Rational Numbers
-7, 24%, 0.2, , 25 5
15
0.3
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event
Examples:
Flipping a coin and it landing on heads
Rolling two number cubes, numbered 1 – 6 and getting ones on
both cubes
An outcome or set of outcomes in a probability experiment.
1
5 31
4 2
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axis of symmetryA line that divides a plane figure
or a graph into two congruent reflected halves
Also called line of reflectionAxis of symmetry (line of reflection)