Types of functions rates of change
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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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Types of Functions, Rates of Change

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Types of functions rates of change

Types of Functions, Rates of Change

Lesson 1.4


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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