TMJC H2 Chapter 1 Graphing Techniques Learning Package 2024

Tampines Meridian Junior College 2024 H2 Mathematics (9758) Chapter 1 Graphing Techniques Learning Package Resources  Core Concept Notes  Discussion Questions  Extra Practice Questions SLS Resources  Recordings on Core Concepts  Quick Concept Checks

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Chapter 1 Graphing Techniques TMJC 2024 Page 1 H2 Mathematics (9758) Chapter 1 Graphing Techniques Core Concept Notes Success Criteria: Surface Learning Deep Learning Transfer Learning  Determine the equations of asymptotes: horizontal, vertical, oblique (if any) of exponential, logarithmic and rational functions.  Find, where applicable, the important features (ASMILE) of a graph.  Identify restrictions on possible values of x and/or y (if any)  Sketch the graph of a rational function such as: ax by cx d += + , 2ax bx cy dx e ++= +  Identify shapes of standard conic curves and state important characteristics of them: ( ) ( ) 2 y k a x h− = − or ( ) ( ) 2 y k a x h− = − ( ) ( ) 22 2x h y k r− + − = ( ) ( ) 22 22 1x h y k ab −− += , ( ) ( ) 22 22 1x h y k ab −− −= or ( ) ( ) 22 22 1y k x h ba −− −= .  Explore the conic APP in the GC to graph a conic section and note the limitations of the conic APPS  Use a GC to graph a given piecewise function  Use a GC to graph a given modulus function  Use a GC to graph a pair of parametric equations  Use GC to find intersection points of graphs  Draw the graph of a given function and label important characteristics such as asymptotes, turning points and intersections with the axes.  Show algebraically that a function cannot lie between 2 certain values (to be determined) and use this information to draw the graph  Convert conic section into standard form (using completing the square or long division)  Use GC (not conic APP) to graph a conic section  Draw the graph of a given piecewise function  Express modulus function as a piecewise function  Draw the graph of a function given in parametric form  Convert the equation of a curve between parametric and Cartesian forms  Sketch graphs of functions with unknowns  Manipulate expressions and make inferences about intersections between graphs Definition of Learning (John Hattie): The process of developing sufficient surface knowledge to then move to deeper understanding such that one can appropriately transfer this learning to new tasks and situations.

Chapter 1 Graphing Techniques TMJC 2024 Page 2 §1 Features of Graphs When sketching graphs, it is important to pay attention to important features. Go through the checklist and take note of each of the following whenever you sketch a graph. 1. Asymptotes (if any) 2. Shape of the graph 3. Maximum/minimum turning points (if any) 4. Intercepts with the axes (if any) 5. Labelling of the graph and axes 6. End points (if any) 1.1 Asymptotes Consider the following curves: (a) e2xy −=+ Obs