Date post: | 19-Dec-2015 |
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Table of Contents
• Graphing Functions & Trend Lines
• Demand, Revenue, Cost, and Profit
• Differentiation
• Integration
• Using Solver
Graphing Functions
• 2 Methods for graphing used:
− Blank Excel file with equally spaced data points (Plotting Points)
− Using Graphing.xlsm file
Plotting Points
• Start with blank Excel file
• Generate 2 columns of data
- one column of x-values
- one column of function values
Plotting Points
• To generate the x-values (in a column)
- Given the interval required
- Given the number of points required
Plotting Points
• To generate the x-values
- Subtract one from number of points needed
- Divide interval length by this number
- This is the length of each subinterval
Plotting Points
• To generate the x-values
- Starting with left endpoint, increase by width of subinterval
- This gives x-value of next point
- Continue until you reach the right endpoint
Plotting Points
• To generate the function values (in a column)
- Type function using an “=”
- Use cell references to replace x
Plotting Points
• Graphing the function
- Use XY-scatter
- Use Smoothed Lines Without Markers
- Label graphs whenever appropriate
Plotting Points
• Ex. Graph the function on the interval [0, 5] using a blank Excel file with 501 equally spaced points.
• Soln:
173 xexf
Plotting Points
• Piecewise-defined functions
- Use IF statement
=IF(statement, rule 1, rule 2)
- statement is a mathematical test
- use rule 1 if the statement is true
- use rule 2 if the statement is false
- AND function can be used within IF statement
Ex. AND(0<=A1,3>=A1) tests if A1 is between 0 and 3
Plotting Points
• Ex. Graph the function
using a blank Excel file with 401 equally spaced points.
41
14322 xx
xxxg
Plotting Points
• Creating a “plotting points” graph in Excel
• Insert, Scatter, Smooth lines• Right click on plot area• Left click on select data• Add data and format graph
Plotting Points
• Can graph multiple functions simultaneously
• Ex. Graph the functions
using a blank Excel file with 701 equally spaced points.
700400601.0
4000202.0
xx
xxxg
0,700on 2000004.0 2 xxf
Graphing.xlsm
• Graphing utility to plot one function
• No cell references used
• Function is typed using the variable x
• Can use parameters (constants) s, t, u, v, or w
Graphing.xlsm
x f (x ) a b stu
vw
31
Formula for f (x )
ConstantsDefinition Computation Plot Interval
FUNCTION
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
x
f (x )
Graphing.xlsm
• Ex. Graph the function on the interval [0, 5] using Graphing.xlsm
• Ex. Use Graphing.xlsm to graph the functions on the interval [-4, 4] using the parameter s = 2, 3, 4, and 5.
173 xexf
sxy