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 Vocabulary The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Angle A shape, formed by two lines or rays diverging from a common point (the vertex). The angle is

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

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

Line Segment A line with two endpoints. Written as

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

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.

Every segment is congruent to its image. 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)

Isometries not only preserve lengths, but they preserve angle measures parallel lines, and betweenness of points

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

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 The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Algebraically A function is even if A function is odd if All of the exponents of the variable are even. A function is odd if All of the exponents of the variable are odd. The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither. A function is neither if The exponents are a mixture of odd and even

All constants really have a x0 BEWARE OF CONSTANTS All constants really have a x0 The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

x0 is EVEN!! The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither.

Graphically 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). A function is odd if The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then it’s Odd. If you get different y’s, then it’s Neither. 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).

Even, Odd or Neither? Ex. 1 Algebraically 1 ODD

Even, Odd or Neither? Ex. 2 Algebraically x0 EVEN

Even, Odd or Neither? Ex. 3 Graphically EVEN

Even, Odd or Neither? Ex. 4 Graphically Neither 

Even, Odd or Neither? 1 x0 EVEN ODD

Even, Odd or Neither? x0 ODD ODD Even

Even, Odd or Neither? 1 1 x0 neither ODD neither

Even, Odd or Neither?  EVEN ODD

Even, Odd or Neither?   EVEN Neither ODD

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?

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