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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.

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constant functions
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
Linear Function
  • Can be represented by
    • Where a and b are constants
  • See Geogebra example
slope and y intercept
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
family of linear functions
Family of Linear Functions
  • Slope = Rate of Change

y=3x + 5

  • Slope = m = 3
  • y-intercept = b = 5
slope and y intercept1

Slope and Y-Intercept
  • The function y = (2/3) * x + 5
  • Slope = 2/3 (up to the right)
  • Y-intercept = 5
linear functions
Linear Functions
  • Consider this set ofordered pairs
  • If we plot the pointsand join them wesee they lie in aline

rate of change

6

3

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

rate of change1
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
Slope
  • When slope =
  • Try y = -7x – 3(predict the results before you graph)
family of linear functions1
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 change2

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 change3
Rate of Change
  • As before, determine therate of change fordifferent sets of orderedpairs
rate of change not a constant
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

GeogebraDemo

function defined by a table
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
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
Results
  • Graph appearsstraight
  • But …rate of change is not a constant
assignment
Assignment
  • Lesson 1.4
  • Page 53
  • Exercises 1 – 65 EOO
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