Question

functions
study guide day 2
date
period
i can determine whether a relation is a function from a table, coordinate pairs, graph, and equation.
20.) ____function
21.) ____vertical line test
22.) ____domain
23.) ____range
24.) ____independent variable
25.) ____dependent variable
a.) all possible x-values of a relation.
b.) an \input\ value of a function.
c.) a relation in which each input has exactly one output.
d.) an \output\ value of a function.
e.) a method to determine if a graph is a function.
f.) all possible y-values of a relation.
state whether each is a function and how you know.
26.)
27.)
28.)
29.)
30.)
31.) (2.2, 9), (1, 2.5), (6.5, 2.25)
32.)
33.)
34.) {((1,3), (2,5), (6,7),(1,4)}
(table, graph, mapping diagram, coordinate pairs are present in respective questions but omitted here as per ocr text processing instructions)

Explanation:

Step1: Match "Function" (20)

A function is a relation where each input has exactly one output. So match with C.

Step2: Match "Vertical Line test" (21)

Vertical Line test is a method to check if a graph is a function. Match with E.

Step3: Match "Domain" (22)

Domain is all possible x - values of a relation. Match with A.

Step4: Match "Range" (23)

Range is all possible y - values of a relation. Match with F.

Step5: Match "Independent Variable" (24)

Independent Variable is the input value of a function. Match with B.

Step6: Match "Dependent Variable" (25)

Dependent Variable is the output value of a function. Match with D.

For 26 (Table):

Step1: Check x - values

In the table, x - values are 1, 5, - 5, 8. Each x has a unique y.

Step2: Conclusion

So it is a function because each input (x) has exactly one output (y).

For 27 (Graph):

Step1: Apply Vertical Line test

Draw vertical lines on the graph. The graph fails the Vertical Line test (it's a parabola opening to the right, so a vertical line will intersect it more than once).

Step2: Conclusion

Not a function, because it fails the Vertical Line test (multiple y for one x).

For 28 (Mapping):

Step1: Check inputs

Inputs: - 3, - 1, 0, 1, 4. Each input maps to exactly one output (- 10 or 10, but each input has one output).

Step2: Conclusion

It is a function because each input has exactly one output.

For 29 (Graph):

Step1: Apply Vertical Line test

Draw vertical lines. Each vertical line intersects the graph at most once.

Step2: Conclusion

It is a function because it passes the Vertical Line test (each x has one y).

For 30 (Mapping):

Step1: Check inputs

Inputs: 2, 3, 4, 7. Input 2 maps to 1 and 2; input 3 maps to 2; input 4 maps to 2; input 7 maps to 2. Wait, input 2 has two outputs (1 and 2).

Step2: Conclusion

Not a function because input 2 has more than one output.

For 31 (Coordinate Pairs):

Step1: Check x - values

x - values are 2.2, 1, 6.5. Each x has a unique y.

Step2: Conclusion

It is a function because each input (x) has exactly one output (y).

For 32 (Table):

Step1: Check x - values

x - values are 1, 2, 3, 4. Each x has the same y (5), but each x has exactly one y.

Step2: Conclusion

It is a function because each input (x) has exactly one output (y).

For 33 (Graph):

Step1: Apply Vertical Line test

Draw vertical lines. Each vertical line intersects the graph at most once.

Step2: Conclusion

It is a function because it passes the Vertical Line test (each x has one y).

For 34 (Coordinate Pairs):

Step1: Check x - values

x - value 1 appears twice (in (1,3) and (1,4)).

Step2: Conclusion

Not a function because x = 1 has two different y - values (3 and 4).

Answer:

1. C. A relation in which each input has exactly one output.
2. E. A method to determine if a graph is a function.
3. A. All possible x - values of a relation.
4. F. All possible y - values of a relation.
5. B. An "input" value of a function.
6. D. An "output" value of a function.
7. It is a function. Reason: Each x - value (input) has exactly one y - value (output).
8. Not a function. Reason: Fails the Vertical Line test (multiple y - values for one x - value).
9. It is a function. Reason: Each input has exactly one output.
10. It is a function. Reason: Passes the Vertical Line test (each x - value has one y - value).
11. Not a function. Reason: Input 2 has more than one output.
12. It is a function. Reason: Each x - value (input) has exactly one y - value (output).
13. It is a function. Reason: Each x - value (input) has exactly one y - value (output) (even though y is same, each x has one y).
14. It is a function. Reason: Passes the Vertical Line test (each x - value has one y - value).
15. Not a function. Reason: x = 1 has two different y - values (3 and 4).