1. Tables vs Graphs

2. Table of Contents
8: Warm-Up, Guided Practice
9: When is a Graph or Table a Function?

3. Warm-Up
Graph the following
y = -2 X Y -2 5 -1 3 1 2 -3

4. Warm - Up
Graph the following 1. X Y -2 5 -1 3 1 2 -3

5. Warm - Up
Graph the following
2. y = -2

6. Learning Intention/Success Criteria
LI: We are learning to understand the difference between using a table and graph to answer questions SC: I know how to -translate a table of values to a graph -gather information about a function from a table -gather information about a function from a graph -determine, in context, whether or not a value represents an x or y value

7. EQ: When is a Table or a Graph a Function?
11/8/201811/8/2018

8. Table
Data arranged in rows and columns
Graph
A diagram that shows the relationship between two sets of numbers
Function
A relationship where each element in the domain (x) corresponds to one element in the range (y)

9. Domain
The values of the independent variable for a function
The values of x
Range
The values of the dependent variable for a function
The values of y

10. Vertical Line Test
A test used to determine if a graph is a function
A graph is a function if there are no vertical lines that intersect the graph at more than one point

11. Worksheet
While talking about his math class, Charles notices that there seems to be a pattern for how long it takes him to do his homework problems, given how many problems he is assigned. He makes a table for the amount of time in minutes, T, based on the number of homework problems, n.

12. Worksheet
While talking about his math class, Charles notices that there seems to be a pattern for how long it takes him to do his homework problems, given how many problems he is assigned. He makes a table for the amount of time in minutes, T, based on the number of homework problems, n.

13. Worksheet 1. What does T(10) represent (in context, not its value)?
T(10) represents how long (in minute) it takes him to complete 10 math problems, which is 9 minutes.
2. What is the value of T(10)? (including units)
9 minutes

14. Worksheet
3. What would it mean if 12 showed up twice in the n column? Would this make sense?
It would mean that he was assigned 12 homework problems on 2 different occasions.
This could make sense because T(12) could have 2 different values depending on how hard the problems are, but it wouldn’t make sense to show up twice

15. Worksheet
4. What would it mean if 15 showed up twice in the T(n) column? Would this make sense?
If 15 showed up twice in the T(n) column, it would mean it took him 15 minutes to complete 2 different amounts of problems. This doesn’t make sense because 2 different homework amounts can’t take the same about to time

16. Worksheet
5. Graph the points from your table on the grid below (be sure to label your axes).
Time (Min)
Number of homework problems

17. Worksheet
6. Do you think that it makes sense to connect the points? Why or why not?
No, because that would mean that he was assigned fractional parts for the number of problems (like 8 ½ problems) which would not make sense.
7. Using your graph, approximately what would you expect to find for T(5).
T(5) = 6.5

18. Reflection What are some advantages to having the graph?
What are some disadvantages to having the graph?

19. Discussion and Reflection
A website shows the official daily high temperature in Kapolei for 2015 in a table of values and also represents the data in a graph. Which representation (table or graph) do you think it would be easiest to see that the temperatures increase, in general, during the summer and decrease in the winter. Explain.

20. Discussion and Reflection
For the same daily high temperatures described in the previous problem, which representation (table or graph) do you think it would be easiest to find the official high temperature on January 30, 2015.

21. Discussion and Reflection
For the same temperatures described in the problem previously, which representation (table or graph) do you think it would be easiest to find all the days where the official high temperature exceeded 85 degrees. Explain.

22. Worksheet
For his birthday, Chaz wants to treat his friends to a day at Game-O-Rama, the local arcade. Since Chaz is on a budget, he needs to figure out how much this party would cost. When he calls Game-O-Rama, the manager tells him that they have special group pricing for his birthday parties. The manager s him the following cost sheet, where n is the number of friends he brings and C(n) is the cost of the party.

23. Worksheet 1. How much would it cost to bring 6 of his friends?
It would cost $35
2. How much would it cost to bring 7 of his friends?
It would cost $35
3. How much would it cost to bring 8 of his friends?
It would cost $40

24. Worksheet
4. What would happen if the same number appeared twice in the n column? For example, what if the next part of the cost sheet looked like this: 13 45 50
The cost would be either $45 or $50. This would be confusing because there are 2 different prices for the same number of people

25. Worksheet
5. On the below grid, plot the points from the first table (the one where n goes up by 12 only).

26. Worksheet
6. Notice that when using only the values of n up to 12, there are never two points with the same first coordinate. Therefore, no two pints lie on the same vertical line. What would happen if you include the two points when n = 13.
There are two different points on the graph when x = 13.

27. Reflection/Discussion
At what point did the last question become a graph of something that is not a function?

28. Guided Practice 1
Is this graph a function?
Yes
B. No

29. Guided Practice 2
Is this graph a function?
Yes
B. No

30. Quiz How do you know if a graph or table is a function?
Give a real life example of a graph or table that is a function
Give a real life example of a table or graph that is not a function.