Math 141

Math 141

1. Chapter 1

   • 1.2 Visualizing Relationships in Data
     • Independent=x-axis, Input, Domain
     • Dependent= y-axis, Output, Range
     • (x,y),(Input,Output)
     • Function: a relation where each input has only one output
   • 1.4 Definition of Function
     • Example of Function: h=5t-3
     • m=-2(t+3)^2, input 2 m=-2(2+3)^2 m=-2(5)^2 m=-50
     • 4 ways to represent a Function, Verbally Symbolically Numerically Graphically
   • 1.5 Function Notation
     • y=f(x) y=output f=name of function x=input
     • f(x)=x^2 F is not a variable
     • f(x)=2x=5 f(1) y=2(1)+5 y=7
   • 1.6 Working with Functions: Graphs
     • If f(6)=3 is a point on the graph, what is the corresponding coordinate pair? (6,3)
     • h(t)=-t^2+3 From here you would plug in the numbers that they give you then plot the points.
   • 1.7 Functions: Getting Information from the graph
     • Domain: [-3,1] Range [-4,0]
   • 1.9 Making and Using Formulas

2. Chapter 2

   • 2.2 Linear Functions: Constant Rate of Change
     • y=mx+b b= y-intercept m= slope
     • g(m)=2-4m ROC: -4 initial value: 2 shape of graph: line slope: -4 vertical intercept: 2
     • j(f)=5 linear: Yes Slope: 0 Vertical-Intercept: 6
   • 2.3 Equations of Lines: Making linear Models
   • 2.4 Varying the Coefficients: Direct Propirtionality Parallel & Perpendicular lines
     • g(t)=4/5t-4 Slope: 4/5 slope of parallel line: 4/5 Slope of perpendicular line: -5/4
     • Direct Proportionality: The Y is directly proportional to the X
     • y=kx k:constant
     • y=-7x constant
     • y=5/6x+9 Not Constant
     • Find slope and equation (-7,0) perpendicular to (-3,6) (5,1)
     • 1-6/5+3 = -5/8 y-0=8/5(x+7) y-0=8/5x+11.2 y=8/5+11.2
     • slope of hornizontal line (-5,8) y=8
     • slope of parallel line (-14,-1) x=-14
     • Let y be directly proportional to x. If x=5 when y=30
     • constant=y/x: k=7
       • equation: y=7x
         • when x=12 y=12(7)=84
           • when y=18/7= 2.57
   • 2.5 selecting & Writing line of Best fit
     • To find the line of best fit you have to make sure that the line goes through 2 or more points
   • 2.6 Linear Equations: Getting Information from a model
     • 5/R-2=4(2Q+1);3
       • 5/3-2=8Q+4
         • =1/8
     • B=2L+2w A=Bxh
   • 2.7 Linear Equations: Points of Intersection
     • Set the two equations equal and dond the x, then plug the x back into each equation
     • photocopier for $5700 maintenance of $15 a month rent for $75 a month each copy would be 3 cents if they rent 6 cents per copy 7000 copies a month
       • 7000 x .03=$210 per month
         • c(x)=5700 + 15x + 210x
           • how many months would the cost be the same?
             • 5700+225x=495x
               • =21 months

3. 7.1 Modeling with systems of Linear Equations

   • Choose the right variables set up a system of equations, solve the system and interpret the results in a sentence
   • x=2+3 4x+9=10
     • Just plug in the x in to the bottom equation
       • Then when you find the x you solve for the y

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