1 2 Analyzing Graphs of Functions and Relations

1. 2 – Analyzing Graphs of Functions and Relations

Example 1: The function f (x) = – 5 x 2 + 50 x approximates the profit at a toy company, where x represents marketing costs and f (x) represents profit. Both costs and profits are measured in tens of thousands of dollars. Use the graph to estimate the profit when marketing costs are $30, 000. Confirm your estimate algebraically.

Example 2: Use the graph of f to find the domain and range of the function. a. b.

Example 3: �

Example 4: Use the graph of to approximate its zero(s). Then find its zero(s) algebraically.

Testing for Symmetry Overview: x-axis: y-axis: Origin:

Example 5: Use the graph of the equation xy = – 6 to test for symmetry with respect to the x-axis, the yaxis, and the origin. Then confirm algebraically.

Example 6: Use the graph of the equation y = –x 3 to test for symmetry with respect to the x-axis, the yaxis, and the origin. Then confirm algebraically.

Even and Odd Functions

Example 7: A. Graph the function f (x) = x 2 – 4 x + 4 using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.

Example 8: B. Graph the function f (x) = x 5 – x 3 + x using a graphing calculator. Analyze the graph to determine whether the function is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.

EXIT SLIP: � Graph the function f (x) = x 4 – 8 using a graphing calculator. Analyze the graph to determine whether the graph is even, odd, or neither. Confirm algebraically. If even or odd, describe the symmetry of the graph of the function.