Math 141 Sections 1,2, and 7.1

Math 141 Sections 1,2, and 7.1

1. Chapter 1

   • Section 1.2
     • Vocabulary
       • Input: Independent Varibale
       • Output: The dependent varibale
       • Independent Variable: Whose variation dose not depend on that of an another
       • Dependent Varibale: Whose value depends on that of another
     • Examples
       • IN {12, 18, 21, 24, 30} OUT {76, 80, 85, 87, 92}
         • This here is showing that every input has one output
       • IN {1, 2, 3, 4, 5, 5.5, 6, 7, 8, 9, 10} OUT {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
         • As you can see this function dose not work because one of the inputs has no output messing up the function
       • The graph on the LEFT shows a relationship of "as the x-axis go up so do the y-axis". The graph on the RIGHT shows "an in consistent graph, no pattern".
   • Section 1.4
     • Vocabulary
       • Function: Every input has one output
         • Four Ways to Represent a Function: Verbally, Symbolically (as an Equation), numerically (in a table), and Graphically
     • Example
       • Vertical Line Test by Graph
         • NO
         • Yes
         • NO
         • If you plug in a number on the x-axis and you get two numbers out on the y-axis then it dose not pass the vertical line test and is not a function
   • Section 1.5
     • Vocabulary
       • Domain: Is the set of all inputs
       • Range: Is the set of all outputs
     • Examples
       • Consider the function f(x)=5x.
         • The name of this function would be called "f"
         • The letter that represents the input would be "x"
         • The output would be "f(x)' or "5x"
         • The rule that be represented would "multiple by 5"
         • If "x" was 3 the solution would be "15"
       • Examples of expressing the given rule in function notion.
         • Divide by 4 and then add 3. (x/4)+3
         • Square, add 2, and then multiply by 5. (x^2+2)*5
         • Multiply by 10, then add 5, and then square. ((x*10)+5)^2
       • Examples of av verbal description to the given function.
         • f(x)=(x/3)+5. Divide by 3 then add 5
         • h(t)=(t+3/5). Add 3 and then divide by 5
       • Examples of Evaluating Functions Let g(x)=x^2-3
         • Let f(x)=(4x^2+5/3)
           • f(1) =((4*(1)^2+5/3) =(9/3) =3
           • f(-2) =((4*(-2)^2+5)/3 =((4(4)+5)/3 =(16+5)/3 =21/3 =7
         • Let g(x)=x^2-3
           • g(-5) =(-5)^2-3 =25-3 =22
           • g(a) =a^2-3
           • g(2) =(2)^2-3 =4-3 =1
   • Section 1.6
     • Examples
       • Graphs of Basic Functions
         • Constant Function f(x)=10 or y=10
         • Identity Function f(x)=x or y=x
       • Graph the following equation, and but it in a table
         • x {-2, -1, 0, 1 ,2 } f(x) {-3, -1, 1, 3, 5}
   • Section 1.7
     • Examples
       • Consider the graph of the function given above. Find the domain and range. Give your answers in interval notation.
         • (x) Domain: {-3,2} (y) Range: [-2,3]
       • Solve for T
         • PV=nRT =PV/nR=T
         • d=rt d/r=t
         • C=3.5+1.5T C-3.5=1.5T T= C-3.5/1.5

2. Chater 2

   • Tool kit A.2
     • Vocabulary
       • Intercal:is a set of real number the correspond geometrically to a line segment
       • Open Interval: From a to b consists of all numbers between a and b excuding the endpoints a and b.
       • Closed Interva: From a to b consists of all numberbetween a and b, including the endpoints a and b.
       • Half-Open interval: From a to b consists of all number between a and b, including one of the endpoints a or b, but not both.
     • Example
       • Consider the interval (-5,1}
         • Verbal description: This is the interval from -5 to 1 including 1 but excluding -5
         • Express the interval in the set builder notation: { x I -5 < x _<_ 1 }
         • Graph the interval
       • Solve the inequality and give your answer in the interval notation
         • 2x+5>99 2x>94 x>47
         • -y>8 y<-8
         • 2k-2>4 2k>6 k>3
   • Section 2.2
     • Vocabulary
       • Linear Function: is a function of the from f(x)=b+mx where "b"and "m" are real numbers. The graph of a linear function is a stright line
       • Rate of Change: of "f" is the constant "m"
       • Initial Value: of "f" is the constant "b"
       • Slope: measures the "steepness" or how quickly a line rises or falls
         • Real Life Example: roof of a house, hill, ramp..
       • Vertical Intercept: The place where the function crosses the y-axis
     • Examples
       • Is the following a linear function? If so then what is the "b" and "m"?
         • f(x)=5-(2/3) Yes b=5 m=2/3
         • g(d)=-(4/5)d+11 Yes b=11 m=-4/5
         • t(h)=(h-7)/15h No Because you could potentially make the equation zero
       • Make a table for the equation W=1200-80x
         • x {0, 1, 2, 3} W {1200, 1120, 1040, 960}
           • Rate of Change would be -80
       • Calculate the slope of the points given
         • (2.3) & (-4,5) m=(5-3)/(-4-2) m=-2/6 m=-1/3
         • (4,8) & (4,-2) m=(-2-8)/ (4-4) m= -10/0
           • Slope is undefined, because zero is in the denominator. m=4 or x=4 would be the solution for this problem
         • (4,-1) & (-6,7) m=(7+1)/(-6-4) m=8/10 m=4/5
   • Section 2.3
     • Slope - Intercept form is y=m+b
     • If you have two points use the equation, y-y2/x-x2
     • x=-3 Slope is equal to undefined
     • y=4 Slope is equal is to zero
   • Section 2.4
     • Parallel = m1=m2
     • Perpendicular m1=-1/m2
   • Section 2.5
     • Best fit line is the line that would best describe a plot of points
     • You can find the slope of a best fit line as well
   • Section 2.6
     • You can find the equation of the a line graphically and algebraically
     • Choose an appropriate variable when constructing linear models
     • When finding a perimeter of a rectangle set the sides equal to the perimeter
   • Section 2.7
     • When finding the intersecting point set the equation of the lines equal to each other
     • Graph two equations to find the point of intersection
     • For the speed in MPH is the amount of miles you will travel in one hour

3. Chapter 7.1

   • Solving systems of equations using the substitution method
     • solve one equation for one variable
     • substitute the expression in the other equation obtaining an equation in one
     • solve for the variable