Download presentation

Presentation is loading. Please wait.

Published bySally Doolittle Modified over 2 years ago

1
Graphs Mathematical Pictures

2
7/9/2013 Graphss 2 How to Visualize Mathematics Graph Visualization of a relationship among variables or data Bar Graph Pie Chart Relational Graph Typical algebraic graph is plot of points in the real plane

3
7/9/2013 Graphss 3 Dow Jones Closing Average Daily closing stock prices for a week Graphs in Everyday Life Question: Is there a trend in stock prices ? 8149 8700 8516 8332 M T W Th F Stock Price in Dollars

4
7/9/2013 Graphss 4 Average daily high temperature Historical daily data points for July Graphs in Everyday Life Question: What is the general trend over July ? 1102031 90 95 100 105 110 Daily High (F°)

5
7/9/2013 Graphss 5 Graphs in Everyday Life Speed-time relationship Travel time as a function of rate (speed) t = d r r t Question: How does travel time relate to speed ?

6
7/9/2013 Graphss 6 Graphs in Everyday Life Temperature scale comparison Conversion of Fahrenheit to Centigrade () C = 5 9 F – 32 FF CC 212 100 32 ● ● Question: How do Fahrenheit freezing and boiling points of water relate to Centigrade points ?

7
7/9/2013 Graphss 7 Graphs in Everyday Life Let’s Review Functions with graphs but no formula DOW Jones Closing Average Average daily temperatures Functions with a formula and a graph Travel time based on rate of travel Conversion of Fahrenheit to Centigrade Question: Do graphs help our understanding ?

8
7/9/2013 Graphss 8 Graphs in Everyday Life Function Characterization What is the common characteristic ? Ordered Pairs – common characteristic of functions (day, average), (day, temperature F ), (student id, name), (speed, travel time), (F, C)(F, C) Question:How do pairs fit graphs ?

9
7/9/2013 Graphss 9 Describing Functions Ordered pairs make graphing easy F = { ( -5, 4 ), ( -2, 1 ), ( 2, 7 ), ( 4, 1 ) } a b (-5, 4) (-2, 1) (2, 7) (4, 1) What is the graph ? … and now? Scatterplot Line graph Question:

10
7/9/2013 Graphss 10 y Function Graphs f = { (x, y) | y = 2x – 1 } x (-1, -3) (1, 1) (2, 3) (3, 5) (4, 7) The Graph of f

11
7/9/2013 Graphss 11 Domain = [ 0, 4 ] Finding Domain and Range Consider: f = { (x, y) | y = 2x – 1, 0 x 4 } x y (0, -1) (4, 7) The Graph of f Range = [ -1, 7 ] Note: For THIS function, the domain and range are closed intervals

12
7/9/2013 Graphss 12 Graphs, Sets and Tables Ordered Pairs and Functions Input Output x y ● ● ● (x, y) Ordered Pair Input Output x y f = { y = 2x + 1 } (x, y) (x, y)

13
7/9/2013 Graphss 13 Graph and Functions Vertical Line Test No vertical line touches the graph of a function at more than one point Function ? YES Function? NO Function? YES ● ● ● ● ● ● ● ● (x 1, y 1 ) (x 1, y 2 ) x = x 1

14
7/9/2013 Graphss 14 Graph and Functions Vertical Line Test Examples Does any vertical line cut the graph more than once ? Function? YES Function? NO Function? YES x y x y x y ● ● ● ● ● ● y = x 2 x = y 2 x = y 2, y > 0

15
7/9/2013 Graphss 15 Think about it !

Similar presentations

OK

1.7 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Graphs.

1.7 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Graphs.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on conservation of natural resources for class 10 Ppt on air water and land pollution Ppt on centring sheet Ppt on exim bank of india 4g wireless systems seminar ppt on 4g Download ppt on indus valley civilization seals Free ppt on autism Ppt on total parenteral nutrition calculations Ppt on lcd tv Ppt on seasonal affective disorder