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Using Graphmatica Graphmatica is a program for drawing all types of graphs. You place a rule in the address bar and a graph is drawn. The rule must be written using x and y variables. Before using Graphmatica you need to know how to change a few things. 1. Go to Labels legends and make the increments for both x and y =1 2. Then go to View Colours and make the background white 3. Then go to ViewGrid range and make the range as shown 4. To clear graphs click Clear Beginning Investigations Investigation 1: Linear rules y = mx + c form. How does the value of m effect the graph? On the one grid get Graphmatica to draw the following graphs. A. y = x B. y = 2x C. y = 3x D. y = 0.5x E. y = 2/3x F. y = -x G. y = -2x Complete: In the general linear form y = mx + c , m represents R…. of C…… for a particular rule. On the graph the value of m changes the G……….. or S…….. Investigation 2: Linear rules y = mx + c from How does the value of c effect the graph On one graph grid get Graphmatica to draw the following graphs A. y = x B. y = x + 1 C. y = x + 2 D. y = x +3 .5 E. y = x - 2 F. y = x - 5 Complete: In the general form y = mx + c The value of c determines the V…………I………. whose coordinates are ( .. , .. ) Investigation 3: Linear rules Special types On one grid get Graphmatica to draw the following graphs A. y = 1 B. y = 5 C. y = -4 D. x = 3 E. x = -2 Complete. All equations of the form y = c produce H…………….Line graphs. All equations of the form x = b will produce V………..Line graphs Source: henchel.graeme.e@edumail.vic.gov.au 6/06/2008 Advanced Investigations Set the grid range as shown Investigation 4: Gradients, Intercepts and Restricted domains On one grid enter the following rules with the extra stuff in the curly braces. Observe the effect of adding the information in the curly braces. A. y = x + 3 {-5, 2} B. y = 4 {0, 6} C. y = -5/4x + 5 {0, 4} Task 1: Determine the rules that will produce the following graphs Hint: To clear the grid lines go to View Colours and make the gridlines white. One of your rules will be y = -7/3x + 7 {0, 3} Use the grid range below Source: henchel.graeme.e@edumail.vic.gov.au 6/06/2008 Investigation 5: Families of rules Put in the following rule: y =a*x {a: 0, 5, 1} and see what happens. Put in the rule y = 2x + a {a: 0, 6, 1} and observe what happens Task 2: Try to determine the rules and construct the following families of graphs Investigation 6: Graphs of inequalities Put the following rules into graphmatica and see what happens A. y < 2x + 3 B. y > x + 4 Task 3: Determine the rules and construct the following diagram. Hint: Two of the rules are written as inequalities and one is specified as a family of lines Really Advanced Investigations: Put in the following Rules y > x^2 and y < 0.5x^2 Put in the following rules (x-3)^2+(y-3)^2<4 and (x+2)^2+(y-2)^2<1 Put in the following rule y < sin(x) and y > sin(2x) + 2 Challenge: Create a smiley face using graphmatica Source: henchel.graeme.e@edumail.vic.gov.au 6/06/2008