1 / 15

Section 1.5

Section 1.5. Functions and Change. Change. The change from A to B is the difference between A and B and is found by subtracting A from B . Change from A to B is given by B - A. Example 1 Finding Change.

sierra-patel
Download Presentation

Section 1.5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1.5 Functions and Change

  2. Change • The changefrom A to B is the difference between A and B and is found by subtracting A from B. • Changefrom A to B is given by B - A

  3. Example 1 Finding Change • Find the change in temperature if the temperature went from F to F.

  4. Relative Change • Relative change is the ratio of the difference between two quantities to the original quantity

  5. Percent Change

  6. Example 2 Finding Relative and Percent Change The table below gives the average health insurance costs paid by employees of a company for years between 1998 and 2003. Find the relative and percent change in the health insurance paid by employees between 1998 and 2003.

  7. Average Rate of Change • This measure uses the ratio of change in one quantity to the change in a second quantity. • An example of average rate of change is miles per hour, which is the ratio of change in distance (miles) to change in time (hours).

  8. Average Rate of Change • Find the average rate of change in the health insurance paid by employees from 1998 to 2003 by finding the ratio of the change in costs to the change in years.

  9. Average Velocity

  10. Example 3 Finding Average Velocity from a Table • The following table gives the height (in feet) above the ground of a ball that was tossed vertically upward at 32 feet per second from a three-story building a. Find the change in height between t = 1.25 and t = 2 seconds. b. Find the relative change and percent change in height between t = 1.25 and t = 2 seconds and interpret. c. Find the average velocity (average rate of change) from t = 1.25 to t = 2 seconds and interpret.

  11. The graph illustrates the height of the ball given in Example 3 against time. Find the average rate of change between the two points shown and interpret. Example 4 Finding Average Rate of Change from a Graph

  12. Average Rates of Change Symbolically • Symbolically, we have

  13. Important Note: • Subtracting both sets of values in the reverse order will result in the same value.

  14. Example 5 Finding Average Rate of Change using Function Notation • The height of the ball given in Example 3 is given by the rule where f(t) is given in feet and t is given in seconds. Use this rule to find the average rate of change of the ball’s height between t = 0.5 second and t = 1 second and interpret the result.

  15. Example 6Interpreting Average Rates of Change • The following table gives the projected world population (in billions) for the given years. Create a line graph of the data. Find the average rate of change between 1950 and 2030 and interpret the result. A line graph is a scatterplot in which the points are connected with line segments.

More Related