Topic: The graphs of mathematical relationships Purpose: To prepare the graph of a relationship expressed in the form of a mathematical equation. Materials: 1-Graph paper 2-pencil 3-rule 4-Calculator (optional) Procedure: Linear relationships: 1-On the same graph paper, prepare the graphs of the following equations: Y= 10XY= 10X + 5 Y = 20X 2- Complete the following table: X 10X 10X + 5 20X 3-Determine the interception of each graph. 4-Determine the slope of each graph. Quadratic relationships: 1-On the same graph paper, prepare the graphs of the following equations: Y = 0.2x2 Y= 0.4x2 Y=5 + 0.2x2 2- Complete the following table: x 0.2X3 0.4X2 5+ 0.2X The inverse relationships: 1-Consists of the equation Y = 2/X. Trace the graph Y v.s X. For this assign to X the following values: 1/2 , 1, 2, 3, 4 and 5. 2-trace the graph Y v.s 1/X. Give X the same values as in the previous step. Discussion questions: What is the relationship between the slope of the graphs and the mathematical equations that generated them? What is the relationship between the slope and the shape of the graph? What is the relationship between the intercept and the shape of the graph?The inverse relationships: l-Consists of the equation Y = 21X. Trace the graph Y v.s X. For this assign to X the following values: U2 , 1, 2, 3, 4 and S. 2-trace the graph Y v.s lr'X. Give X the same values as in the previous step. Discussion questions: What is the relationship between the slope of the graphs and the mathematical equations that generated them? What is the relationship between the slope and the shape of the graph? What is the relationship between the intercept and the shape of the graph? If X represents time and Y repressents the distance traveled by a given object, hov.r are the three curves interpreted? If X represents time and Y represents the velocity of a given object, how are the three curves interpreted? 3 For each of the anteriores equations, make the graph Y versus X. 4For each of the above equations, make the graph Y versus X2 Conclusion questions: 1) What shape do the Y v.s X graphs have? 2) What is the shape of the Y v.s ngraphs? 3;. If Y is the distance traveled by an object and X is the time it takes for the object to travel that distance, how are the three graphs interpreted? Discussion questions: 1-What is the shape of the curve Y v.s X? 2-What shape does the curve Y v.5 UK have? 3If Y is the pressure and X is the volume, how is the graph Y v.5 X interpreted