1. Functions
LT:
I will be able to explain the graph with a real-life scenario
Think of three things you can do to help insure your success in this class
I can …
I can…
Today’s Agenda
Success Criteria I can create graphs to explain a real-life scenario
Do Now
Lesson
Activity

2. Graphing in Two Dimensions
Speed
Time

3. Two Dimensional Graphs
Two dimensional graphs show the relationship between two variables. For example, a graph could show a person’s distance from an object as he moves around during a specified period of time. Can you think of any other relationships that could be graphed? The next few slides give examples to illustrate what these graphs look like.

4. A train pulls into a station and lets off its passengers.
Speed
Speed
Time Elapsed
Time Elapsed
Discussion topics
Time is independent (continues without interruption)
Speed is dependent constant, decreasing, increasing
Top left; constant speed and then slow down instantly and gone: not a function because time stopped
Top right: correct
Bottom left: increasing and decreasing speed over time
Bottom right: constant speed, then crash to complete stop in an instant (not good and not a function)
Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7
Speed
Speed
Time Elapsed
Time Elapsed

5. A man takes a ride on a ferris wheel.
Distance from ground
Distance from ground
Time Elapsed
Time Elapsed
Discussion topics
Time is independent (continues without interruption)
Distance is dependent
Top left; going back in time (not a function)
Top right: correct
Bottom left: up and down, but never back to the top
Bottom right: going back in time (not a function)
Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7
Distance from ground
Distance from ground
Time Elapsed
Time Elapsed

6. A woman climbs a hill at a steady pace and the starts to run down one side
Speed
Speed
Time Elapsed
Time Elapsed
Discussion topics
Time is independent (continues without interruption)
Speed is dependent: constant, decreasing, increasing
Top left: correct constant speed and then speeds up down
Top right: speeds up and then slow down (would be a graph of height vs time)
Bottom left: increasing and then constant speed
Bottom right: increases then decreases and then increases forever
All are functions, can someone explain why they are all functions?
Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7
Speed
Speed
Time Elapsed
Time Elapsed

7. A child swings on a swing.
Distance from ground
Distance from ground
Time Elapsed
Time Elapsed
Discussion topics
Time is independent (continues without interruption)
- Distance is dependent
All are functions, explain to your partner why all are a function
Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7
Distance from ground
Distance from ground
Time Elapsed
Time Elapsed

8. A child climbs up a slide and then slides down.
Speed
Speed
Time Elapsed
Time Elapsed
Discussion topics
Time is independent (continues without interruption)
Speed is dependent: constant, decreasing, increasing
Top left: increasing speed, constant, decreasing
Top right: not a function, why
Bottom left: correct
Bottom right: constant speed, then decreasing speed
Ask students if they remember what makes a function or not from 8th grade? If not goal is to have then be able to explain by slide 7
Speed
Speed
Time Elapsed
Time Elapsed

9. Students pick to be Sully or Mike
They are asked to graph the distance from the entrance with respect to time.
(one part of the movie does not show the 2 characters so tell students to assume both characters keep walking away from the door)
Remind students that their pencil/pen should keep moving across the graph because time continues
Might need to show the clip 2 to 3 times so students can try, then think through the second time, and then make their final version the 3rd time

10. How far from the entrance?
Distance from door
Time
Have a few students present and talk through what is happening
Remember creating functions so moving away from entrance, standing still, or moving toward entrance

11. They are asked to graph the speed of Dash during the race.
Remind students that their pencil/pen should keep moving across the graph because time continues
Might need to show the clip 2 to 3 times so students can try, then think through the second time, and then make their final version the 3rd time

12. How fast does Dash run? Speed Time
Speed: increasing, decreasing, constant

13. How far above the ground are Wesley’s feet?
Wesley is the character with the mask

14. How far above the ground are Wesley’s feet?
Height
Started up and ended lower: so if started at (0,0) quadrant 1 and 4 or if started up at time 0 then only need quadrant 1
What about the loop around the branch? (remember no going back in time)
Time

15. Students will be asked to graph height vs timeOr
Speed vs time

16. Watch Spidey go!
Height vs. Time
Speed vs. Time
Speed
Height
Time
Time

17. Height of Neville above the ground vs time

18. How high is Neville?
Height above ground
Time