1. 2022 Graphing Techniques (For Upload)

CJC MATHEMATICS DEPARTMENT 2022 JC1 H2 MATHEMATICS (9758) TOPIC: GRAPHING TECHNIQUES Page | 1 H2 MATHEMATICS TOPIC GRAPHING TECHNIQUES 2022/JC1 Content Outline  Use of a graphing calculator to graph a given function.  Sketching graphs with important characteristics such as symmetry, intersections with axes, turning points and asymptotes of the following:  ax bycx d  2ax bx cydx e   Determine the equations of asymptotes, axes of symmetry, and restrictions on the possible values of x and/or y. 1 Introduction Have you seen graphs (bar, pie, histogram, line) in newspapers, television, magazines and books etc.? The purpose of the graphs is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Thus graphs are visual representations of data collected. Data can also be presented in the form of a table; however a graphical presentation is easier to understand. In the H2 Mathematics syllabus, graphing calculator (G.C.) will aid in the sketching of graphs. However, students should be aware that there are limitations inherent in G.C. G.C. Basics: Before sketching a graph, ensure that the settings are as shown. Settings can be accessed by pressing mode . . (Use the arrow keys to navigate and enter key to highlight FUNCTION.)  Self-Reading G.C. can be used to sketch the graphs of the following basic curves: Equation Press Input Screen Result 2y x y= X,T,,n x2 graph brings us to the input screen for specifying equations displays the plotted graph (of the specified equation)

CJC MATHEMATICS DEPARTMENT 2022 JC1 H2 MATHEMATICS (9758) TOPIC: GRAPHING TECHNIQUES Page | 2   Equation Press Input Screen Result 3y x y= X,T,,n ^ 3 graph To zoom in at the point  0, 0, press : zoom 2 enter yx y= 2nd x2 X,T,,n graph 1yx y= 1  X,T,,n graph Alternative: Use alpha y= 21yx y= 1  X,T,,n x2 graph Alternative: Use alpha y= 3y x y= math 4 X,T,,n graph exy y= 2nd ln X,T,,n graph exy y= 2nd ln () X,T,,n graph 3 e e

CJC MATHEMATICS DEPARTMENT 2022 JC1 H2 MATHEMATICS (9758) TOPIC: GRAPHING TECHNIQUES Page | 3 Equation Press Input Screen Result lny x y= ln X,T,,n graph  Remark: Due to the limitation of G.C., there might be a difference between what we see on the zoom 6: ZStandard screen and the actual graph that we draw. Take for example lny x: We should be familiar with the other zoom functions keys available in the G.C. so that we can use them to obtain an optimal view of the graph. Nevertheless, we should take note that G.C. is simply a tool that is used to determine the general shape of a curve. 2 Features of Graphs In this section, we will investigate the following features of graphs:  Axial intercepts  Asymptotes  Turning points  Lines of Symmetry  Possible range of values of x