1 / 17

What Makes a Function Linear

What Makes a Function Linear. Lesson 1.3. What Is A Line?. Check out this list of definitions or explanations to the question Define Line Today we look at what makes a function linear. Rate of Change. Consider example y = 3x + 5 We note the rate of change is constant

vin
Download Presentation

What Makes a Function Linear

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. What Makes a Function Linear Lesson 1.3

  2. What Is A Line? • Check out this list of definitions or explanations to the question • Define Line • Today we look at what makes a function linear.

  3. Rate of Change • Consider example y = 3x + 5 • We note the rate of change is constant • This means it is a linear function • It graphs as a straight line y=3x + 5

  4. Plotting Points on the Calculator • Use Data Matrix on Calculator • Choose APPS, then 6 Data/Matrixthen NEW

  5. Starting Up • Choose DATA • Give it a variablename for savingin memory

  6. Cursor must be here Enter formula here Entering Data • Enter numeric values in the cells • Enter a formula at the top • Using column name

  7. Viewing Data • Note the results of the formula • We can do further calculations • We can also plot these points

  8. Choose line type Specify the columns for the X and Y values Plotting Data • Choose F2 for Plot SetupScreen • Then F1 for Define

  9. Plotting Data • Goto the Y= Screen to turn off any functions there • Then specify ZoomData • This fits the window to the limits of the data

  10. Plotting Data • Note the graph includes the points we had in the data matrix • It is a line-graph, the points are represented by boxes

  11. Another Example • Consider the following table of values • Note the value of for any two pairs of values

  12. Example From Text $20,000 • See Example 2, pg. 19 • Formula used for depreciation Value of equipment = original value – $4000 * number of years • To generalize:Dependent Qty = startValue + rateOfChange * independentQuantity

  13. Family of Linear Functions • Slope = Rate of Change View TI Nspire filewhich demonstrates the slope-intercept formula y=3x + 5 • Slope = m = 3 • y-intercept = b = 5

  14. Family of Linear Functions • Calculating slope with two ordered pairs (X2, Y2) • (X1, Y1) • Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

  15. Warning • Not all functions which appear linear will actually be linear!! • Consider the set of ordered pairs • Graph them • Decide whether graphis linear • Check slope for differentpairs

  16. Results • Graph appearsstraight • But …rate of change is not a constant

  17. Assignment • Lesson 1.3 • Page 24 • Exercises1 – 5, 7, 9, 13, 15, 19, 21, 23

More Related