Transcript Draw six segments that pass through every dot in the

Which is heavier?
Warm-up – April 1, 2013
• Construct an x-y table and graph for
each:
• 1. f(x) = 2x -3
• 2. g(x) = x2 + 1
• 3. g(x) = x2 + x + 1
• 4. g(x) = x3 - 1
Math is brought to you by
the number …
•April 1, 2013
•Day 57 of 90
•90-57 =
Interactive Notebook
p31 MCC912.A.REI.1 Explain each step in
solving a simple equation as following from
the equality of numbers asserted at the
previous step, starting from the assumption
that the original equation has a solution.
Construct a viable argument to justify a
solution method.
P33 MCC912.A.REI.3 Solve linear
equations and inequalities in one variable,
including equations with coefficients
represented by letters.
EOCT
EOCT
EOCT
EOCT
Unit 5
Vocabulary
Angle
• A shape, formed by two lines or rays diverging from
a common point (the vertex).
The angle is
ABC
Circle
• The set of points on a plane at a
certain distance, or radius, from a
single point, the center
Perpendicular Line
Two lines that intersect at a right angle (90°).
Written as
AB  PQ
Parallel Line
Lines in a plane that either do not share any points
and never intersect, or share all points.
Written as AB PQ
Line Segment
A line with two endpoints.
Written as
AB
Point
An exact position or location in a given plane.
Point A
or
Point B
Line
The set of points between points P and Q in a
plane and the infinite number of points that
continue beyond the points.
Written as
AB
Distance along a line
The linear distance between two points on a
given line.
Right Angle
An angle that measures 90°.
Acute Angle
An angle measuring less than 90° but greater
than 0°.
Obtuse Angle
An angle measuring greater than 90° but less
than 180°.
One-to-One
A relationship wherein each point in a set of
points is mapped to exactly one other point.
Pre-image
The original figure before undergoing a
transformation.
Image
The new, resulting figure after a transformation
Isometry
A transformation in which the preimage and
image are congruent.
Transformations are called RIGID if
every image is congruent to its
preimage.
Rigid transformations can also be
referred to as an ISOMETRY.
Every segment is congruent to its image.
Which of the following are rigid
transformations? (Isometry)
Find the value of each variable,
given that the transformation is
an isometry.

72 
10
6 x
3y  2
x  12, y  4
Congruent
Figures are congruent if they have the same
shape, size, lines, and angles.
Similar Triangles
Triangles are similar if they have the same
shape but have different sizes.
Even and
Odd
Functions
Algebraically
A function is even if
All of the exponents of the variable are even.
A function is odd if
All of the exponents of the variable are odd.
A function is neither if
The exponents are a mixture of odd and even
BEWARE OF
CONSTANTS
All constants
0
really have a x
0
x is
EVEN!!
Graphically
A function is even if
The graph reflects across the y-axis
(means you can fold it hotdog style and it would match up).
A function is odd if
The graph has 180 rotational symmetry
about the ORIGIN
(means you could turn it upside-down & it would still look the
same...it must go through the origin).
Ex. 1 Even, Odd or Neither?
Algebraically
f ( x)  x  x
3
1
Ex. 2 Even, Odd or Neither?
Algebraically
f ( x)  x  1
2
0
x
Ex. 3 Even, Odd or Neither?
Graphically
Ex. 4 Even, Odd or Neither?
Graphically

Even, Odd or Neither?
f ( x)  2 x  3
4
x0
1
f ( x)  x  x
3
Even, Odd or Neither?
f  x   x
3
f  x  5x
3
f  x   x  4x0
2
Even, Odd or Neither?
1
0
x
f  x   x  x f  x  x  2x f  x   x  4x  1
3
2
3
3
1
Even, Odd or Neither?

Even, Odd or Neither?


If the dots shown are part of an
even function, what points are
also on the function?
If the dots shown are part of an
odd function, what points are also
on the function?
HW
Practice WS