In section 2.7, we will modify the equations of the “basic” functions and see what effect these modifications have on the graphs of the modified functions. Next, we will also learn how to classify functions as odd, even or neither And finally, we will test a given function for possible symmetries of its graph about the x-axis, the y axis, or about the origin Note: For this Section, I recommend that you FIRST study the materials from the text and then supplement your understanding of the topic by going over the examples given below in these notes and also studying th The possible modification that we can do to the graph of y = f(x) are: • Shift (or translate) the graph horizontally left or right • Shift(or translate) the graph vertically up or down • Reflect the graph about the X axis • Reflect the graph about the Y axis • Vertically stretch or shrink the graph • Horizontally stretch or shrink the graph The textbook has covered these with examples in great details and has also summarized all the modifications in a table form. The title of this table is ” Summary of Graphing Techniques” and it is given at the very end of this section, just before the exercise set. Use the text to first LEARN these modifications. You need to know them well enough so that given any function equation you can do the following: • • Identify the corresponding basic function and draw its graph Identify all modifications done to a basic function and sketch the corresponding graph. Note: These modifications do NOT change the shape of the original graph Objective Given the equation of a function, to be able to identify the corresponding ‘basic’ function and then graph the equation. Examples Below are listed some sample problems. As all the graphs in this set have the same basic shape, their graphs have not been included. Summary Table refers to the Table titled ” Summary of Graphing Techniques” given at the end of this section in the text Sample Problems The ‘basic function’ for each of these problems is y = f(x) = |x|. The graph of y = |x| is shaped like the letter ‘V’ with its vertex at (0,0)