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Graphing Functions

Mathematics for Business Decisions, part II. Graphing Functions. Math 115b. Ekstrom Math 115b.

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Graphing Functions

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  1. Mathematics for Business Decisions, part II Graphing Functions Math 115b Ekstrom Math 115b

  2. Graphing Functions Exercise: • Using only your calculator, sketch a graph of the function • Use only 13 equally-spaced points • Graph over the interval [0,6] • Use the whole area of graph paper Ekstrom Math 115b

  3. Graphing Functions Ekstrom Math 115b

  4. Graphing Functions Ekstrom Math 115b

  5. Graphing Functions Ekstrom Math 115b

  6. Graphing Functions Plotting Points • Need to produce graphs that are well-formatted as well as informative • We can have Excel do this for us • Excel needs many points to graph accurately • Many is a relative term Ekstrom Math 115b

  7. Graphing Functions Example 1 • We have a function • Let’s have Excel graph this function over [0,4] • We need values of f (x) to do this – how can we get them? Ekstrom Math 115b

  8. Graphing Functions Determining Points for Graph • Want a “large enough” number of points • arbitrary number • if graph is not pretty, you didn’t choose enough • with use of computers, can’t have too many • The text chooses 501 points so it evenly divides the interval where x0= 0 and x500= 4 • Note: We have 501 points since we start at x0 Ekstrom Math 115b

  9. Graphing Functions Determining Points, cont. • We now have to determine what the distance between any 2 adjacent points • (4-0)/500 = 0.008 • The distance between any 2 adjacent points is 0.008 • For any graph, the distance between any 2 adjacent points within the interval (a,b), subdivided by n pointswill be: Ekstrom Math 115b

  10. Graphing Functions Graph Examples.xls • Now that we have the number of points we need and the distance between any 2 adjacent points, we need to have Excel graph the function • Need to use the IF function to generate y-values • IF(statement, rule 1, rule 2) • If the statement is true, IF uses rule 1; else it uses rule 2 • We will use rule 1 to be and 0 to be rule 2 • Our statement will be • Let’s look at Graph Examples.xlsto see how Excel graphed the function using our points Ekstrom Math 115b

  11. Graphing Functions Graphing • Once we have the values of f (x) that we need, we can have Excel generate a graph for us • Go to Chart Wizard and choose XY Scatter plot, with no markers (or if you have the template, use the Scatter plot Template) • We must enter our data range for the y-values and then change the series to show the x-values • Let’s try Ekstrom Math 115b

  12. Graphing Functions Example 1 =IF(A3<1,0,IF(A3<=3,-0.75*(A3)^2+3*A3-2.25,0)) Ekstrom Math 115b

  13. Graphing Functions Graphing Several Functions • You can also have Excel graph multiple functions on one set of axes • Doing so helps us understand the connections between the quantities that are represented • Think back to Project 1: Need a Demand curve, Revenue curve, Cost curve, and Profit curve • To do this, you will follow all the previous steps that you did to graph one function Ekstrom Math 115b

  14. Graphing Functions Graphing Several Functions • You need to determine how many points you need for each function you want to graph • Also, you need to determine the distance between any 2 adjacent points • Have Excel determine the y-values for each x-value by using the IF function Ekstrom Math 115b

  15. Graphing Functions Example 2 • If your functions were and you wanted Excel to graph them over the interval [0, 2000], what would your IF statements be for each? • Let’s see what the graphs look like Ekstrom Math 115b

  16. Graphing Functions Example 2 Ekstrom Math 115b

  17. Graphing Functions Graphing Utility • To create your own graphs can be time consuming (although very valuable) • A graphing utility, Graphing.xlsx, has been provided to you in the course files • Open up the file and follow the directions in the blue box • Note: This file contains macros which you need to enable – if you cannot produce a graph, you may not have enabled the macros • A backup, Graphing BU.xlsxhas also been provided (just in case) Ekstrom Math 115b

  18. Graphing Functions Practice • You should practice working with the graphing utility, Graphing.xlsx • Use example functions that have been given in the text • You know what these graphs look like • There are also exercises in the text that you can try • You should know what the graphing utility is doing • Know why you are entering specific items into each cell Ekstrom Math 115b

  19. Graphing Functions Practice • Exercise 1 Start with a blank Excel file and use 701 evenly spaced points to plot the graph of over the interval [-12,12]. Recall that Excel uses EXP(x) for . • Exercise 11 Use Graphing.xlsxto plot the graph of over the interval [-12,12]. Ekstrom Math 115b

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