Chapter 1, 2 and 7.1

Chapter 1, 2 and 7.1

1. Chapter 1

   • Vocab
     • Dependent: Y- Axis/ Range
       • Independent X-Axis/ Domain
         • Ordered Pair (x,y)
           • Function- one input gives one output
   • Examples
     • Function
     • C=32+5x
       • The cost to order team shirts is $32 plus $5 per shirt ordered. The cost C of the order is a function of the number x of shirts purchased
     • Types of Functions
   • Inequalities
     • {x|1<x<4}
       • This equation would expressed in interval notion as (1,4). Also on the graph it would have a open circle that points to the right.
     • [3,5]
       • The data set represented in this example would be graphed with a filled in circle at 3 and goes to the right.
   • Function Notation
     • Simple as putting f(x) in front of equation rather than a Y=

2. Chapter 2

   • Constant rate
     • Rate of Change= Slope
   • Linear vs. Non-Linear
     • Linear Anything with X that isn't being divided or square rooted
       • Example: 3x+2
       • Example: x
     • Non- Linear: Square roots, X is the denominator, or the exponent is cubed
       • Example: 4/3m +5
   • Models
     • Slope- Intercept Form: y=mx+b
     • Point-Slpoe Form:y-y1=m(x-x1)
     • General Form: 0=Ax+Bx+Cx
   • Slope
     • Can be zero, undefined or have a simple slope.
     • Directly proportionality= y=kx
     • Y- Intercept isn't clear
       • If your Y intercept is undetermined plot to points and do y2-y1/x2-x1
     • Y/X
   • Vertical and Horizontal Lines
     • Vertical when X equals a number
       • Slope is undefined
     • Horizontal when Y equals a number
       • Slope is 0
   • Line of Best Fit
     • Match the most points along the line of best fit
   • Constructing Linear Models
     • 0=-4x+45
       • An aircraft is approaching an international airport. Using radar, an air traffic controller determines that the linear equation D=-4x+45 models the distance D (measured in miles) of the approaching aircraft from the radar tower in x minutes since the radar identified the aircraft. How many minutes will it take for the aircraft to reach the radar tower?
       • 10.5 Minutes
   • Points at Which They Intersect
     • Set the equations equal and then use answer then solve for remaining variable

3. 7.1

   • Substitution Method
     • (11,2)
       • x-1/2y +3. &nbsp;Solve the system 8x+3y=-11 Plug -1/2y+3 in for x and solve for Y, once completed then do the same for X
   • Elimination Method
     • (-5,-2)
       • Solve the system: 3x+5y=-25 4x-7y+-6 Times the eqautions to find a common multiple of 12. Next eliminate one of the coeficciants and once complete plug your value of solved coefficient for the undetermined coeficciant.&nbsp;
   • No Solution/ Inconsistent
     • When 0 equals a number
       • 0=8
   • Infinitely Many Solutions
     • When everything cancels
       • 0=0
   • One Solution
     • Where lines intersect, this is normal and most likely to happen.

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