Lesson 3

Sometimes it is useful to determine the equation of a function given its graph. Equation from a Graph describes this process.

From the video, you can summarize the steps for determining the equation of the function from its graph.

Step 1: Determine the maximum and minimum values of the graph. Use these values to determine the midline and the amplitude. These are the a- and d-values of the function.

 and

Step 2: Determine the period of the graph. The parameter b can be calculated by the formula

Step 3: Determine c by choosing the function y = sin x or y = cos x. If y = sin x, then c is the distance away from the y-axis to the first intersection of the graph with the midline where the graph is increasing. If y = cos x, then c is the distance away from the y-axis to the first maximum point.

Step 4: Substitute the parameters into the standard form of the function.

Use these steps to help you complete the following Self-Check questions.

Self-Check 3