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.

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Unit 5 Unit 5 VocabularVocabular

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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

6767767767767767767767767767767767767767 767

Parallel Line

Lines in a plane that either do not share any points and never intersect, or share all points.Written as AB PQ

6767767767767767767767767767767767767767 767

Line Segment

A line with two endpoints.Written as

AB

Point

Point A or

Point B

An exact position or location in a given plane.

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 67777777777777 7

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.

Rigid transformations can also be referred to as an ISOMETRY.

Every segment is congruent to its image.

Transformations are called RIGID if every image is congruent to its preimage.

Which of the following are rigid transformations?

(Isometry)

Find the value of each variable, given that the transformation is an isometry.

72x6 23 y10

4 ,12 yx

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 Even and Odd Odd

FunctionFunctionss

AlgebraicallyAlgebraicallyA function is even if

A function is odd if

All of the exponents of the variable are even.

All of the exponents of the variable are odd.

A function is neither ifThe exponents are a mixture of odd and

even

BEWARE OF

CONSTANTSAll constants

really have a x0

x0 is EVEN

!!

GraphicallyGraphically

A function is even if

A function is odd if

The graph reflects across the y-axis (means you can fold it hotdog style and it would match up).

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).

f x x x( ) 3

Even, Odd or Neither?Ex. 1Algebraically

1

f x x( ) 2 1

Even, Odd or Neither?

Algebraically

Ex. 2

x0

Ex. 3 Even, Odd or Neither?

Graphically

Ex. 4 Even, Odd or Neither?

Graphically

4( ) 2 3f x x 3( )f x x x

Even, Odd or Neither?

x0

1

Even, Odd or Neither?

x0 3f x x 35f x x 2 4f x x

Even, Odd or Neither?

1 x0 3 2f x x x 3 2f x x x 3 4 1f x x x 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?

HWHWPractice WS