Transcript opposite of a number

A function can be
represented by a list
of ordered pairs.
{(-1, 2), (-2, 3),
(-3, 4), (-4, 5)}
scalene triangle
A triangle with no congruent sides.
Scalene
Not Scalene
reflection
A transformation that reflects, or
“flips”, a graph or figure across a line,
called the line of reflection.
Line of reflection
6
5
4
G
F
3
2
H
1
-8 -7 -6 -5 -4 -3 -2 -1 0
-1
-2
I
-3
-4
-5
-6
G'
H'
1 2
3 4 5
I'
F'
6
7 8
A function can be represented
by a verbal description.
Use words to describe
the functional
relationship.
x
-1
0
1
The y-values for a set of
points are 4 more than
twice the corresponding
x-values.
y
2
4
6
isosceles triangle
A triangle with at least two
congruent sides.
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
-3
-9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
-3 is the opposite of 3
-3 + 3 = 0
6
7
8
9
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
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'
A
B
D
B'
C
D'
C'
Quad ABCD  Quad A’B’C’D’
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
domain
The 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}
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
The origin is
the center
of dilation.
9
8
B'
7
6
5
4
A'
A
-9 -8 -7 -6 -5 -4 -3 -2 -1
3
2
1
-1
-2
-3
-4
-5
B
1 2 3 4 5 6
7 8
9
C
C'
-6
-7
-8
-9
Triangle ABC is
transformed into triangle
A’B’C’ by the dilation
using scale factor of 2
x
range
The 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}
A function can be
represented by a table.
f(x) = -2x + 3
x
-1
0
1
2
y
5
3
1
-1
midpoint of a line segment
Point that lies halfway between the
segment’s endpoints and divides it
into two congruent parts y
To find the
midpoint, find the
average of the
coordinates of the
endpoints of the
line segment
6  4 4 + (  2)
,
2
2
M(-1 , 1)
9
8
7
A(-6, 4)
M(-1, 1)
-9 -8 -7 -6 -5 -4 -3 -2 -1
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
1 2 3 4 5 6
7 8
B(4, -2)
9
x
probability
• Probability is a measure of how
likely an event is to occur.
• Probability of an event occurring
must be from 0 to 1.
3
Ex: A number cube has faces
numbered from 1 to 6. The
probability of rolling an odd
5
3
1
=
number is 3 out of 6, or
.
6
2
1
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
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.
Triangular Prism
Lateral face
Base
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
translation
A transformation that shifts or
“slides” every point of a figure or
graph the same distance in the same
6
direction.
G
FGH is
translated 5
units to the
right and 3
units down to
F’G’H’.
5
4
F
3
H
-8 -7 -6 -5 -4 -3 -2
2
G'
1
F'-10
-2
-3
-4
-5
-6
1 2
3 4 5
H'
6
Cylinder
Three-dimensional figure with
two congruent circular bases
and a curved surface
Base
Curved
surface
Base
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.
y
The origin is
the center
of dilation.
9
8
7
6
5
4
3
2
1
A
A'
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
B'
B
1 2 3 4 5 6
C'
7 8
C
-6
-7
-8
-9
Triangle ABC is transformed
into triangle A’B’C’ by the
dilation using scale factor of ½.
9
Cross product
• One way to solve a proportion
is to use the cross product.
x 3
=
14 2
2 x =3 14
2x = 42
x = 21
Rational Numbers
• Numbers that can be written as the
a
ratio of two integers, b , where b  0.
• Integers are the set of all positive and
negative whole numbers, and zero.
Rational Numbers
-7, 24%, 0.2,
0.3
25  5
Not Rational Numbers
,
15
event
An outcome or set of outcomes in a
probability experiment.
Examples:
Flipping a coin and it
landing on heads
Rolling two number
cubes, numbered 1 – 6
and getting ones on
both cubes
1
5
3
1
4
2
axis of symmetry
A line that divides a plane figure or
a graph into two congruent
reflected halves
Also called line of reflection
Axis of symmetry
(line of reflection)