Chapter+4


 * __4.1__**

2 (-,+) **I** 1(+,+) --- **I** --- 3 (-,-) **I** 4 (+,-)

Ordered pair- (x,y) coordinates to a graph quadrant- part of a graph midpoint- (0,0)

**__4.2__**

**What is a more basic way to say translation?** Change **Do you have any information about how to move the image?** (x,y) -> (x+a, y+b) **Did you make a note about when the x value changes in a translation?** The x value changes when a number is added to it **What about how it changes?** Added to/Subtracted from **Which direction?** Left/Right **Did you make a note about when the y value changes in a translation?** The y value changes when a number is added to it  **What about how it changes?** Added to/Subtracted from **Which direction?** Up/Down **Can you give an example of a translation in real life?** moving seats in the classroom (you choose to move yourself (the point) to a different seat (the coordinates)) **More** **basic way to say reflection** **:** Mirror Image **W** **hat the image needs to reflect over** **:** **x over y or y over x** **Information about how to move the image:** if it is over the y axis you are changing the x values and vice versa **W** **hen the x value changes in a reflection** **and** **how it changes:** the x values only change if the shape is moved over the y axis **How the y value changes in a reflection:** the y values only change if the shape is moved over the x axis **Can you give an example of a reflection in real life?** when you look in a mirror **M** **ore basic way to say dilation** **:** Size **H** **ow to move the image** **:** (x,y) -> (nx, ny) **E** **xample of a dilation****in real life** **:** **How the x value changes in a dilation:** When it is multiplied by a number **What about How does it change:** It will get smaler or bigger **Which direction does it change:** Outwards/Inwards **Did you make a note about when the** **y** **value changes in a dilation?** When it is multiplied by a number **H** **ow** **does** **it changes** **:** It will get smaler or bigger **W** **hich direction** **does it change:** Outwards/Inwards **More** **basic way to say rotation** **:** turn **H** **ow to move the image** **:** pivot the figure around one axis **How** **the image needs to rotate around** **:** around a certain point **G** **ive an example of a rotation in real life** **:** the moon around the earth (if the moon didn't rotate around its own axis)
 * **__transformation__** - movements of geometric figures
 * **__preimage__** - the position of the figure before the transformation
 * **__image__** - the position of the figure after the transformation
 * **__reflection__** - A figure is flipped over a line
 * **__translation__** - A figure is slid in any direction
 * **__dialation__** - A figure is enlarged or reduced
 * **__rotation__** - A figure is turned around a point

**__4.3__** **‍Represent relations as sets of ordered pairs, tables, mappings, and graphs.** **‍Find the inverse of a relation**


 * ordered pairs - coordinates on a graph
 * tables - chart that shows data
 * mapping - make 2 circles, label one x (domain) and one y (range) put the ordered pairs in numerical order, draw arrows that match up the ordered pairs again

(1,6) (2,3) (4,7) (5,19) (2,19)

__domain__ __range__ 1 3 2 6  4 7  5 19  (add your arrows to match up the coordinate points)


 * graphs - chart to show data
 * inverse - the flipped fraction ex. 1/2=2/1 or (4,3) and (3,4)

**__BAT:__** **when you graph an inverse the graph will have a point with it's reflection in the oposite quadrant- 1 to 2 and 3 to 4**

**__4.4__**


 * solution - answer to a problem
 * solution set - a few numbers that could be the right answer (one of them is right)
 * equation in two variables - //y// = 3 //x// – 5

***When you're given an equation, turn it into a chart for x and y coordinates. Then graph the ordered pairs! 3x=5y 3x-5y=0 // f(x)=y // //f(x)=2x+5 is the same as y=2x+5//
 * Slope Intercept- y=mx+b
 * Standard Form= ax+by=c (any equation that can be written in this form is linear)
 * Exponential equation- the equation has an exponent

**__4__** **__.5__**


 * linear equation - the equation of a line
 * standard form - Ax + By = C, where A __>__ 0, A and B are not both zero, and A, B, and C are integers whose greatest common factor is 1.
 * slope intercept form - //y = mx + b//

**__4.6__**


 * function A relation in which each element of the domain is paired with exactly one element of the range. (doesn't have duplicated x-values.)
 * vertical notation If any vertical line passes through no more than one point of the graph of a relation then the relation is a function.

**__4.7__**

terms- parts of an equation
 * arithmetic sequence- find the pattern numbers progress in using an equation ex. *2, +2, /2, -2 (in and out chart)
 * sequence- finding the orders numbers progress in ex. *2, +2, /2, -2 (in and out chart)
 * common difference- The difference between each number in an arithmetic series.

**__4.8__**


 * inductive reasoning The process of making a conclusion based on a pattern of examples
 * deductive reasoning The process of using facts, rules, properties, or definitions
 * look for a pattern