Graphing Calculator Tutorial

Transcription

1 Graphing Calculator Tutorial This tutorial is designed as an interactive activity. The best way to learn the calculator functions will be to work the examples on your own calculator as you read the tutorial. Open the graphing calculator and begin. Calculator Perform the following examples on your calculator: To enter a negative number such as -5, click the number then the key. To clear the last entry, enter. To clear all data, enter. Use the key to express an exponent. To evaluate an exponential expression such as 2⁵ click the following keys:. The calculator preserves normal operator precedence and performs calculations following the order of operations: parentheses are performed first, followed by powers and exponents, multiplication and division, and then addition and subtraction. Precedence Name Operator 1 Parentheses ( ) [ ] { } 2 Powers and Exponents ^ 3 Multiplication and Division / 4 Addition and Subtraction + Enter the expression 5 + 6² * 2 10, and then click the equals sign. The answer is 67. The calculator performed the steps in the following order: 5 + 6² * *

2 Special care must be used when entering expressions with parentheses. Everything in the window will be inserted into parentheses when the button is clicked. Enter on your calculator. Notice the entire expression, 5 + 6, is inside the parentheses. An expression with parentheses such as (3 5) must be entered in the following order to be calculated correctly:. The correct answer is -8. To correctly evaluate the expression 4 2(8 5). First, evaluate parentheses. Click. Next, perform multiplication by -2. Click. Finally add 4. Click. The expression equals -2. Shared Features - Equation Plotter and Curve Fit It is possible to adjust the coordinate plane's viewing window by adjusting the axis scaling or by moving the position of the coordinate plane. The Zoom menu allows you to select the axis parameters you want to adjust. Both selects the x- and y-axes simultaneously. X selects only the x-axis. Y selects only the y-axis. 2

3 The key will zoom in on the graph so it decreases the axes scaling. The key will zoom out on the graph so it increases the axes scaling. The roller on the mouse will also increase/decrease the axes scaling. The key returns the graph to the default scaling between 1 and -1. Select the Equation Plotter tab. Select Y on the Zoom menu. Place your cursor on the coordinate plane and use your mouse roller to change the y-axis scaling between -300 and 300. Select X on the Zoom menu. Use the keys to adjust the x-axis scaling between -0.5 and 0.5. Reset the viewing window. If the axes scaling is between -10 to 10, the axes up, down, left, and right. keys move the coordinate Select the Curve Fit tab. Set the y-axis parameter from -5 to 5. Set the x-axis parameter from -5 to 5. Use the arrow keys to adjust the coordinate axes up, down, left, and right. Reset the viewing window. Clicking and dragging the viewing screen will move the visible portion of the graph regardless of the axes scaling. 3

4 Select either the Equation Plotter or Curve Fit tab. Drag the viewing window so only Quadrant I is visible. Reset the viewing window. The Step menu allows you to designate the place value of the numbers in the ordered pairs. None and.01 generate x- and y-values to the hundredths place..1 generates x- and y- values to the tenths place. 1 generates integer x- and y- values. Trace names ordered pairs along a graph. Select either the Equation Plotter or Curve Fit tab. Set Both axes parameters from -10 to 10. Select 1 on the Step menu. Move the cursor around the viewing window to see its effect on the ordered pair in the upper left corner. Repeat for each Step option. Reset the viewing window. Continue to the examples on the next page. 4

5 Curve Fit The Curve Fit utility allows you to create a scatter plot and a line of best fit. You can enter up to three separate sets of data using the Plot tabs. All data sets will be shown simultaneously. Perform the following example on your calculator using the points (100, 4), (155, 5), (198, 6), (257, 7): Select the Curve Fit tab. Select the Plot 1 tab. Set x-axis scaling between 0 and 300 to accommodate the data's domain. Set y-axis scaling between 0 and 10 to accommodate the data's range. Select to add a point to the table. Select a cell within the table and enter a number using the keyboard on your computer. Use the tab or arrow keys on your keyboard to move from cell to cell. Enter the ordered pairs (100, 4), (155, 5), (198, 6), (257, 7) into the table. Press Enter when finished. To delete a data point from the table, select the point's row and then click. Try deleting the point (198, 6). Adjust the viewing window using the mouse roller. Check the table to see if any random points were added. Delete these extra points before continuing. This step must be repeated any time you adjust your viewing window while using the Curve Fit utility. The Fit menu allows you to select a desired trendline for a data set. Select each Fit menu option to view its effect on the graph of the current data. Select to clear all data. Reset the viewing window. Alternatively, you can click directly on the graph to enter ordered pairs. 5

6 Select the Curve Fit tab. Set both axes scaling between -10 and 10. Set the Fit menu to No Fit. Set the Step menu to 1. Click anywhere on the coordinate plane and add four or five data points. Notice the points appear in the table as well as on the coordinate plane. Select Clear. Select a different setting for the Step menu. Add 5 new points to the graph. Select Linear on the Fit menu. The line that appears is a line of best fit, i.e., the line that minimizes the distance from all data points. Look at the equation expressed in the window on your calculator. The equation in the window on your calculator will be different from the one above. The equation represents the line of best fit on the graph. 6

7 Add more points to your graph. Notice how the additional points change the equation values. Add a few more points. Notice how the additional data points modify the trendline. Further, look at the value at the far end of the equation window. This number represents the order of the equation. Currently it displays a value of 1, showing the equation is a first order equation or best linear fit. Use the up/down arrows to change the order of the equation used to approximate the data. Return the equation order to 1. Clear the data. Reset the viewing window. The up/down arrow keys allow you to approximate functions using higher-order trendlines. First Order (n = 1) Second Order (n = 2) Third Order (n = 3) Equation Plotter The Equation Plotter allows you to graph up to six functions simultaneously. A function must be entered correctly into one of the function dialog boxes labeled f(x), g(x), h(x), r(x), p(x), or q(x) to view its graph. The independent variable's coefficient, operator, and the variable x must be used before the calculator will graph the function. 7

8 Perform the following examples on your calculator: Select the Equation Plotter tab. Example 1: Graph the function y = 5x. Using your computer keyboard type 5*x in the f(x) dialog box and press Enter. Example 2: Graph the function f(x) = -x. Type -1*x in the g(x) dialog box and press Enter. Example 3: Graph the function y = x + 4. Use parentheses to enclose fractions. Type (-1/2)*x + 4 in the h(x) dialog box and press Enter. Notice you cannot see the line. Adjust the axes scaling until the blue line is visible. Example 4: Graph the function p = g The calculator will only recognize x as the independent variable, so replace the g with x when entering the equation in the dialog box. Type (4/5)*x 17.2 in the r(x) dialog box and press Enter. If you cannot see the line, adjust the viewing window until the yellow line is visible. To delete a single function, highlight the function in the dialog box, press Delete on the keyboard, and press Enter. Delete the function y = x + 4. If the line did not delete from the viewing window, be sure you press Enter. Select to clear all dialog boxes and graphs. Continue to the example on the next page. 8

9 Select the Equation Plotter tab. Reset the axes scaling. Enter -x and -1*x in the equation dialog boxes. Notice the effect the operator has on creating (and not creating) a graph. y = -x (without * operator) y = -1*x (with * operator) Continue to the example on the next page. 9

10 Clear the calculator. Reset the axes scaling. Enter function y = 1/x into a dialog box. Put your cursor on the coordinate plane and use your mouse roller to change the axes scaling until the graph becomes visible. before scaling (mouse roller) after scaling If a function does not graph, check that you have entered an operator, used a lowercase x, and have pressed Enter. Also, check that the viewing window parameters are properly set to view the function. Continue to the examples on the next page. 10

11 How to Find the Intersection of Two Functions Select the Equation Plotter tab. Clear the calculator and Reset axes scaling. Enter y = 5x and y = -x into the Equation Plotter utility. Select Trace from the Step menu. Move the cursor onto one of the lines. The cursor will turn blue. Move the cursor to the intersection point. The cursor will turn red at the approximate intersection point. Notice the intersection of these two functions occurs at (0, 0). The Trace function does not always return the exact intersection point. It may be necessary to use other algebraic methods to check the accuracy of the intersection value. How to Generate a Table of Values for a Function Perform the following example on your calculator: Delete the function y = -x. Enter y = 5x into a dialog box and select. Set the Start value at -15 and the End value at 15. Set the Step value to 1 and press Enter. The table names ordered pairs on the line. Experiment with other Start, End, and Step values to see the effect on the table. You have completed a review of the calculator features used in the Algebra I: course. The calculator has several features you will not utilize in this course. An introduction to these features is included on the following pages. 11

12 You may continue with the tutorial to familiarize yourself with these additional capabilities or you may stop here and begin the course. You may print this document and keep it handy to use as a reference as you work through Algebra I:,. Additional Features - Calculator Reciprocals To invert a number or fraction, simply enter the number and click the reciprocal button reciprocal function returns the reciprocal value in decimal form.. The Degrees and Radians When entering trigonometric functions, be aware if you have selected to return your answer in degrees or radians. Trigonometric Functions (sin, cos, tan, sin -1, cos -1, tan -1 ) To calculate any of the trigonometric functions, click the number, click the function key you want to use, e.g.,, and click the equals sign. Exponential and Logarithmic Functions (e x, log, ln) To calculate exponential or logarithmic functions, click the number, click the function key, e.g.,, and click the equals sign. To calculate a power of ten, click the power, then click. Radicals and Fractional Powers (, ) To calculate square and cubed roots, click the number and click the function key, e.g.,. For fractional powers (n th roots of x), type the base number, click the number, then click the equals sign. key, click the root 12

13 Value of Pi Obtain the constant Pi by clicking the key. Additional Features - Equation Plotter Graphing Functions A number of built-in functions are available for graphing. Utilize the following table when graphing special functions. Function name Command Examples Power 10^x 10 x, 2 -x, (1/2) x Logarithmic log(x) log(x), log(2*x) Exponential exp(x) e x, e -2x, (1/2)*e x/2 Natural Logarithm ln(x) ln(x), ln(3*x), ( (ln(x/5) )^3 Open the Equation Plotter utility. Set Both axes scaling between -3 and 3. Enter each function in an equation dialog box and view its graph: ln(x) exp(x) log(x) 10^x (1/2)^x 3*(x + 1.5)^2 +.5*x 1 13 Copyright 2009 The American Education Corporation. A+, A+LS, and A+nyWhere Learning System are either trademarks or registered trademarks of The American Education Corporation