Compare the domains and ranges of these functions with your results in Question 3. Complete the graph so that it is the graph of an even function. Explain why it is the graph of an even function. Complete the graph so that it is the graph of an odd function. Explain why it is the graph of an odd function.
Students verify their conclusions using a table and algebraically.
They describe the connections between symmetry of the graph of the function, entries in the table of values for the function, and the function's symbolic form. Then students mentally estimate the coordinates of the maximum and minimum points that occur between consecutive roots and refine their estimates by using the trace feature of the calculator. Students use their understanding of the continuity of this function to explain why the function must have a minimum or a maximum point between consecutive roots. Use a calculator to generate a table of values for and a graph of each function. For each function give two intervals on which the function is continuous.