Activities

1.  A function has one _____________ for every _______________.

2. Does the following set of coordinate points describe a function, yes or no?

(3, 4), (6, 7), (5, 2), (1, 19), (0, -4), (11, -6), (4, 8), and (2, 2)

3. Does the following set of coordinate points describe a function, yes or no?

4. Does the graph below display a function, yes or no?

5. Does the graph below display a function, yes or no?

6. Do the following set of coordinate points comprise a function?

(1, 0), (0, -1), (-1, 0), (1, -1), (-1, 1), (0, 0), (1, 1

7. Which coordinate point needs to be removed in order to make this into a function?

(1, 5), (9, 3), (-1, 2), (4, 8), (11, -1), (12, -1), (5, 2), (8, 7), (-2, 0), (-25, 11), (4, 7), (127, -2)

8. Is this set of coordinate points a function, yes or no?

(2, 0), (1, 2), (2, 0)

9. Does the graph below display a function?

10. Look at the graph on the coordinate plane below. Is it a function?

11. Is this graph a function, yes or no?

12. Explain why the following graph is not a function.

13. Christina created the following piecewise graph. Is it a function?

14. Does the graph below represent a function?

15.  Does the graph below represent a function, yes or no?

16. Insert the numbers 2, 3, 4, and 5 into the table below (each once) in order that the table represents a function.

17. Is the following graph a function, yes or no?

18. Create a graph that is a function, includes two open circles, at least one arrow, and three curved lines that do not connect.

19. Given the relation y = x², and the domain {-2, -1, 0, 1, 2}, does the relation describe a function, yes or no?

20. Graph the function on a coordinate plane or graphing calculator. Do you think it is a function, why or why not?

21. The graph below is not a function. Determine an input value where there are two output values.

22. The line connecting the points (3, 5) and (3, -2) is not a function. How can you tell by finding its slope?

23. Only two capital letters would be considered functions when placed on the coordinate plane. Which ones are they?

24. Graph the line y = 0x – 3 and the point (-3, 0). Could your graph represent a function? Why or why not?

25. Below is a graph of the stock market from 1990 until 2013 broken down into quarterly segments. Explain why the graph must be a function.

Answer Key/Rubric

1. Output, input

2. Yes

3. No

4. Yes

5. No

6. No

7. (4, 8) or (4, 7)

8. Yes

9. No

10. Yes

11. Yes

12. It does not pass the vertical line test. In other words, at least one input, in this case 8, has more than one output, in this case -7 and 7.

13. No, the input x=5 has two outputs

14. Yes

15. Yes

17. No

19. Yes

20. Yes, it is a function because although near the x-value of zero it looks like the graph becomes vertical. It actually get’s closer and closer to zero without ever touching the x=0 vertical line. Thus, strictly speaking, no vertical line passes through the graph of y = 1/x at any two points.

21. The graph fails the vertical line test for any value from x = -5 to x = 9; those inputs have more than one output

22. When using the slope formula for the points (3, 5) and (3, -2) the result has a denominator, which is zero. Thus, the slope for the line connecting those points is undefined, which means that the line itself is vertical. Finally, since a vertical line contains all possible output values for a single input value, it is not a function.

23. V and W

24. The graph is not a function because at the input value of -3, the line has an output of -3 and the point has an output of 0. Thus there are two outputs for the input -3 and the graph is not a function.

25. The stock market graph must be a function because for each input, that is, for each month or year (or in our case quarter), there must be only one output. There cannot be two values for the stock market at the end of a given quarter. Thus, even if the values from quarter to quarter do not change, for each input there is only one output.