Chapter+2


 * __**Roles of Wiki**__ || __**Student #1**__ || **__Student #2__** ||
 * **Editor** || **//=== //**T. Landis === || //put your first initial and last name// ||
 * **Multimedia** || H.Longnecker ||  ||
 * **Text** || S. Hagen ||  ||
 * **Practice Problems** || R. Jackson ||  ||
 * **Career/Real Life App** || M. Herring || S. Warner ||

PERIOD 2

Helpful: Good definitions Put answers down for examples or else it’s pointless

Enjoyed: The definitions The vocab was helpful

Comments: Everything was “smooshed” together, hard to pick out important info b/c it ran together All one font and color Very,very plain – no pictures Need videos Tanner whining

**TEXT**
 -__Relation__ - The mapping, or pairing, of input values with output values. -__Domain__ - The set of input values (x). -__Range__ - The set of output values (y). -__Function__ - A relation when there is exactly one output for each input. -__Slope__ - The ratio of vertical change to horizontal change (rise over run). -__Slope Formula__ - __y‚ - y„__ x‚ - x„ -__Parallel__ - Lines that do not intersect. -__Perpendicular__ - When lines form 90° angles. -__Steepness__ - - If two lines are positive, then the largest slope (m) is steepest. - If two lines are negative, then the largest absolute value of the slope (|m|) is the steepest. - If two lines are parallel, then the slope and steepness is the same. - If two lines are perpendicular, then the slopes at opposite recipricals, and the largest is the steepest. -__Slope-intercept Form__ - A linear equation. y = mx + b; m = slope and b = y-intercept. -__Y-intercept__ - The point of a line that crosses the y-axis. -__X-intercept__ - The point of a line that crosses the x-axis. -__Standard Form__ - A linear equation. Ax + By = C; A and B are both not zero. -__Point-slope form__ - y - y‚ = m(x - x‚); m = slope and (x‚, y‚) = point. -__Direct Variation__ - when two variables show y = kx or k = y/x and k does not equal 0. -__Constant of Variation__ - The k value that remains the same. -__Scatter Plot__ - A graph used to determine whether there is a relationship between paired data. -__Positive Correlation__ - When x and y values increases. __-Negative Correlation__ - When x values increase and y values decrease. -__Relatively No Correlation__ - When there is no linear pattern. -__Linear Inequality__ - When two variables can be writen as Ax + By < C, Ax + By __<__ C, Ax + By > C, or Ax + By __>__ C. -__Solution (of Linear Inequality)__ - When an ordered pair make the inequality true. -__Half Planes__ - The shaded area on a coordinate plain which contains the solutions. -__Piecewise Function__ - A function represented by a combination of equations, each corresponding to the domain. -__Step Function__ - A piecewise function that resembles steps. -__Absolute Value Function__ - A piecewise function. -__Vertex__ - The corner point of a function on the graph.
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**__//Practice problems!!!!!//__** 2.1 Functions and their Graphs Example You can represent a relation with a table of values or a graph of ordered pairs.

|| 0 || 1 || 3 || || 5 || 3 || 4 ||
 * X
 * Y

Graph the relation. Then state whether it’s a function. 1. || -4 || 7 || 3 || || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">6 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">-3 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">4 ||
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">X
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">Y

<span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">2. || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">6 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">5 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">11 || || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">-4&9 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">3 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">5 ||
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">X
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">Y

<span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">2.2 Slope and Rate of Change Example You can find the slope of a line passing through 2 given points. Points: (4,2) and (-3,5) Slope: m= __y2 - y1__ = __5-4 = -1__ x2- x1 -3-4 7 Find the slope of the line passing through the given points. 1. ( 2,4), (5,7) 2. (5,3), (0,0) 3. (1,5), (6,0)

2.3 Quick Graphs of Linear Equations Example You can graph a linear equation in slope-intercept form or in standard form.

Linear __Standard Form__ Y=-3+1 4x-3y=12 Slope= -3 x-intercept= 3 y-intercept= 1 y-intercept= -4

Graph the equation 1. Y= -x+3 2. -3x+y= 5 3. 6x-y= 2

2.4 Writing Equations of Lines Example You can write an equation of a line using (1.) the slope and y-intercept, (2.) the slope and a point on the line, or (3.) two points on the line.

1. Slope-intercept form, m=2, b=-3 y=2x-3 2. Point-slope form, m=2, (x1,y2) = (2,1) y-1=2(x-2) y= 2x-3 3. Points (0,-3) and (2,1) slope= __1-(-3)__ = 2 2-0 Y=2x-3 Write and equation of the line that has the given properties. 1. Slope: -1, y-intercept: 2 2. Slope: 3, y-intercept: (-4,1) 3. Points: (3,-8), (8,2)

2.5 Correlation and Best-Fitting Lines Example You can graph data to see what relation, if any, exist. The table shows the price, p (in dollars per lb ) of bread where t is the number of years since 1990.

|| <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">0 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">1 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">2 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">3 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">4 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">5 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">6 || || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.70 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.72 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.74 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.76 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.78 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.84 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">.87 ||
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">T
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">P

<span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">Approximate the best-fitting line using (4, .80) and (6, .85), __.85-.80__ y=-.80=.025(x-4) m= 6-4 =.025 y=.025 + .70

Approximate the best fitting line for the data. 1. || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">14 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">11 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">21 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">3 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">4 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">19 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">10 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">1 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">17 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">6 || || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">4 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">6 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">1 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">10 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">9 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">0 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">5 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">10 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">2 || <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">7 ||
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">X
 * <span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">Y

<span style="color: rgb(18, 13, 13); font-family: Arial,Helvetica,sans-serif">2.6 Linear Inequalities in Two Variables Example You can graph a linear inequality in 2 variables in a coordinate plane. To graph Y<x+2, first graph the boundary line, Y=x+2. Use a dashed line since the symbol is <, and not __<__. Test the point (0,0) __is__ a solution of the inequality, shade the half-plane that contains it. (Right)

Graph the inequality in a coordinate plane. 1. 2x<6 2. Y__>__ -x+4 3. Y __<__ 7

2.7 Piecewise Functions Example You can graph a piece wise function by graphing each piece separately.

Y={ x-1, if x<0 ¬ Open circle { -x+2, if x__>__0 ¬ closed circle Graph y= x-1 to the left of x=0 Graph y=-x+2 to the right of and including x=0 Graph the function. 1. Y= {2x, if x<-1 {2x+1, if x__>__-1 2. Y= {-x, if x__<__0 {3x, if x>0

2.8 Absolute Value Functions Example You can graph an absolute value function using symmetry. The graph of **__y= 3 [ x +1 ] -2__** has vertex (-1, -2). (to find the vertex of the equation, the b=y and x= the opposite of the number inside the parenthesis.)(slope = 3) Plot a second point such as (0,1). Use symmetry to plot a 3rd point,(-2, 1). Note that a=3>0 and [a] >1, so the graph opens up and is narrower than the graph of y= [x]. 1. Y= -[x] +1 2. Y= [x-4] +3 3. Y= 3[x+6] -2 Edited by Tanner Landis
 * note: [ ] = absolute value symbols.

Someone please post some stuff in this. This project needs to be done like pronto. -Tanner

<span style="color: rgb(244, 31, 31); font-family: 'Comic Sans MS',cursive; background-color: rgb(252, 252, 252)"> <span style="color: rgb(244, 31, 31); font-family: 'Comic Sans MS',cursive; background-color: rgb(252, 252, 252)">**MATH STUFF HERE>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>**

<span style="color: rgb(51, 246, 40)"><span style="font-family: Georgia,serif">**October 26, 2008 4:36 pm.......still no** <span style="background-color: rgb(255, 255, 255)"> **entries**   <span style="color: rgb(36, 240, 20)">-editor