Chapters 1, 2, &7.1

Chapters 1, 2, &7.1

1. Chapter 1

   • Section 1.2
     • Input
       • Independent Variable
       • x
         • Domain
       • how far left and right the line goes
     • Output
       • Dependent Variable
       • y
         • Range
       • how far up and down the line goes
     • Relation
       • (x,y)
     • Scatterplot
   • Section 1.4
     • Function: each input only get one output
       • Outputs can have many inputs
       • y to any odd powered exponent is a function
       • y=3(10)^2 + 5--> 3(100)+5-->300+5-->y=305
   • Section 1.5
     • [ ] means the number is included
     • ( ) means the number is not included
       • [3, ∞ )
     • input x --> Function f --> output f(x)
       • y=2x^2 +3
         • g(x)=2x^2+3
       • g(x)^2 -3 and g(2)
         • g(2)=2^2 -3
           • g(2)=4-3
             • g(2)=1
   • Section 1.6
     • Toolkit A.2 & C.3
       • open interval: less than or greater than, open dot, ( )
       • closed interval: less than or equal to AND greater than or equal to, shaded dot, [ ]
       • half open interval: all number between a and b but only include one or the other NOT BOTH
       • FLIP SIGN WHEN DEALING WITH A NEGATIVE
     • Constant Function--> horizontal line
       • y=10 OR f(x)=10
     • Identity Function--> diagonal line
       • y=x OR f(x)=x
   • Section 1.7
     • g(x) --> given x and are looking for y
   • Section 1.9 and Toolkit C.1
     • Formula: equation involving variables
       • PEMDAS is backwards when solving equations

2. Chapter 7, Section 1

   • Substitution Method
     • Solve for one variable
       • Substitute
         • Back-Substitute and Solve
           • 2x+y=1
             • y=1-2(-2)
               • y=5
                 • Intersect at the point (-2,5)
         • 3x+4y=14
           • 3x+4(1-2x)=14
             • 4-5x=14
               • -5x=10
                 • x=-2
       • 2x+y=1 y= 1-2x
     • 2x+y=1 AND 3x+4y =14
   • Elimination Method
     • Adjust coefficients
       • Add/Subtract Equations
         • Back Substitute
           • x-2y=2
             • 4-2y=2
               • -2y=-2
                 • y=1
                   • Intersect at (4,1)
         • 4x=16
           • x=4
       • When needed
     • 3x+2y=14 AND x-2y=2
   • Graphical Interpretations
     • One Solution (consistent)
       • Intersect at a single point
     • No Solution (inconsistent)
       • Parallel Lines
     • Infinitely Many Solutions
       • One line

3. Chapter 2

   • Section 2.2
     • linear function: y=mx+b
       • y=24x+18
     • rate of chnage = slope = m
       • rise/run
         • y/x
       • y2-y1/x2-x1
         • 2-1/3-1
           • 1/2
       • x = undefined
       • y = 0
     • initial value = y-intercpet = b
   • Section 2.3
     • Point-Slope Form
       • y-y1=m(x-x1)
     • Slope-Intercept Form
       • Slope: 1/2 and y intercept (0,3)
         • y=3+1/2x
     • General Form
       • Ax+By+C=0
       • 7x+4y+10=0
   • Section 2.4
     • Parallel lines have the same slope
     • Perpendicular lines have negative reciprocals of slopes
       • y=2x +2
         • Slope is 2
         • Negative Reciprocal is -1/2
     • Constant of Proportionality
       • y is directly proportional to x
         • y = kx
           • y = mx
   • Section 2.5
     • Line of Best Fit
   • Section 2.6
     • Choose an appropriate variable for unknown numbers
       • Express all quantities given in terms on the variable
         • Express the mode as a function of the variable
           • y=750-.0075x
         • where y is the total miles driven
       • x and y; t and w
   • Section 2.7
     • b1+m1x=b2+m2x
       • 6+2x=6x+2
         • Setting two equations to each other

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