2024 JPJC Chapter 5 Graphing Techniques II

Jurong Pioneer Junior College Mathematics (9758) JC 1 - 2023 Chapter 5 Graphing Techniques II (Students’ Version) / Pg 1 Content outline :  Effect of transformations on the graph of y = f(x) as represented by y = af(x), y = f(x)  a,  fy x a  and y = f(ax), and combinations of these transformations  Relating the graphs of  fy x ,  fy x , and   1 fy x to the graph of  fy x References  http://www.h2maths.site [This website offers Applets which allow self-exploration of numerous types of graphs covered in this topic. Refer to "Transformation of Graphs" under the link "Graphs and Functions" in this website]  H2 Mathematics For 'A' Level, Federick Ho, David Khor, Yui-P'ng Lam, B.S. Ong Volume 1, Call No 510.76 HO  Mathematics The Core Course for A-level, L Bostock and Chandler, Call No 510 BOS  MEI Structured Mathematics (2nd Edition), Pure Mathematics 4, Terry Heard and David Martin, Call No 510 HEA  Pure Mathematics 4, Hugh Neill and Douglas Quadling, Call No 510 NEI Prerequisites  Coordinate geometry from Add Maths  Using GC to draw simple curves from Chapter 2 Graphing Techniques I  Functions learnt in Chapter 4  O Level Trigonometry Chapter 5: Graphing Techniques II

Jurong Pioneer Junior College Mathematics (9758) JC 1 - 2023 Chapter 5 Graphing Techniques II (Students’ Version) / Pg 2 1.1 Translations (I) Graphs of the form y = f(x) + a Example 1 The diagram below shows the graphs of 2y x , 2 5y x  and 2 3y x  on the same axes. How are the graphs of 2 5y x  and 2 3y x  related to the graph of 2y x ? Solution: The graph of 2 5y x  is obtained by translating the graph of 2y x ____________ ______________________________________ The graph of 2 3y x  is obtained by translating the graph of 2y x ____________ ______________________________________ This can be generalized as follows: For a > 0, the graph of y = f( x) + a is a translation of the graph of y = f( x) by a units in the positive y direction, the graph of y = f(x)  a is a translation of the graph of y = f(x) by a units in the negative y direction. Note: This transformation affects the y-coordinates only. The x-coordinates remain unchanged. Example 2: Given the graph of y = f(x) below, where f(x) = 2 4 2 x , sketch, on separate diagra