Loading in 5 sec....

Types of Functions, Rates of ChangePowerPoint Presentation

Types of Functions, Rates of Change

- By
**king** - Follow User

- 58 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Types of Functions, Rates of Change' - king

**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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Types of Functions, Rates of Change

Lesson 1.4

Constant Functions

- Consider the table of ordered pairs
- The dependent variable is the same
- It is constant

- The graph is a horizontal line

Linear Function

- Can be represented by
- Where a and b are constants

- See Geogebra example

Slope and Y-Intercept

- Considering y = m * x + b
- The b is the y-intercept
- Where on the y-axis, the line intersects

- On your calculator
- Go to Y= screen
- Enter at Y1 (2/3) * x + 5
- Predict what the graph will look like before you specify F2, 6 for standard zoom

Slope and Y-Intercept

- The function y = (2/3) * x + 5
- Slope = 2/3 (up to the right)
- Y-intercept = 5

Linear Functions

- Consider this set ofordered pairs
- If we plot the pointsand join them wesee they lie in aline

•

•

•

•

Rate of Change

- Try calculating for differentpairs of (x, y) points
- You should discover that the rate of change is constant … in this case, 3

GeogebraDemo

Slope

- When slope =
- Try y = -7x – 3(predict the results before you graph)

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?

You may need to specify the beginning x value and the increment

Rate of Change- Consider the function
- Enter into Y= screen of calculator
- View tables on calculator (♦ Y)

Rate of Change increment

- As before, determine therate of change fordifferent sets of orderedpairs

Rate of Change (NOT a constant) increment

- You should find that the rate of change is changing – NOT a constant.
- Contrast to thefirst functiony = 3x + 5

GeogebraDemo

Function Defined by a Table increment

- Consider the two functions defined by the table
- The independent variable is the year.

- Predict whether or not the rate of change is constant
- Determine the average rate of change for various pairs of (year, sales) values

Warning increment

- 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

Results increment

- Graph appearsstraight
- But …rate of change is not a constant

Assignment increment

- Lesson 1.4
- Page 53
- Exercises 1 – 65 EOO

Download Presentation

Connecting to Server..