Types of Functions, Rates of Change

1 / 18

# Types of Functions, Rates of Change - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

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

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
• 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
Family of Linear Functions
• Slope = Rate of Change

y=3x + 5

• Slope = m = 3
• y-intercept = b = 5

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

6

3

Rate of Change
• Given function y = 3x + 5

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

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?

Rate of Change
• Consider the function
• Enter into Y= screen of calculator
• View tables on calculator (♦ Y)
Rate of Change
• As before, determine therate of change fordifferent sets of orderedpairs
Rate of Change (NOT a constant)
• You should find that the rate of change is changing – NOT a constant.
• Contrast to thefirst functiony = 3x + 5

Function Defined by a Table
• 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
• 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
• But …rate of change is not a constant
Assignment
• Lesson 1.4
• Page 53
• Exercises 1 – 65 EOO