Question

6.1 function vs nonfunction

1. consider the relation:

{(2,5),(4,7),(2,9),(6,1)}
a. is this relation a function?
b. explain your reasoning.
2.

x	y
-3	4
-1	6
2	4
5	9
-1	8

a. is this relation a function?
b. identify the input that causes a problem, if any.
3.
a graph shows points at:
(-4,2),(-1,5),(2,5),(2,-3),(5,1)
a. is this graph a function?
b. describe how you know using the vertical line test.
use the graph to the right.
4.

• 1→3
• 2→5
• 3→7
• 3→9
• 4→11

a. is this relation a function?
b. explain why or why not using the definition of a function.

Explanation:

Step1: Analyze relation 1 inputs

Check x-values: $2, 4, 2, 6$

Step2: Apply function definition (1a)

A function has unique x-inputs. $x=2$ repeats.

Step3: Explain reasoning (1b)

Input $2$ maps to $5$ and $9$.

Step4: Analyze table 2 inputs

Check x-values: $-3, -1, 2, 5, -1$

Step5: Apply function definition (2A)

$x=-1$ repeats, so not a function.

Step6: Identify problematic input (2B)

The repeating x-value is $-1$.

Step7: Analyze graph 3 inputs

Check x-values: $-4, -1, 2, 2, 5$

Step8: Apply function definition (3a)

$x=2$ repeats, so not a function.

Step9: Apply vertical line test (3b)

A vertical line at $x=2$ hits 2 points.

Step10: Analyze relation 4 inputs

Check x-values: $1, 2, 3, 3, 4$

Step11: Apply function definition (4a)

$x=3$ repeats, so not a function.

Step12: Explain via definition (4b)

Input $3$ maps to $7$ and $9$.

Answer:

1. a. No

b. The input $2$ is paired with two different outputs ($5$ and $9$).

1. A. No

B. $x=-1$

1. a. No

b. A vertical line drawn at $x=2$ would intersect the graph at two points $(-2, 5)$ and $(2, -3)$, which fails the vertical line test.

1. a. No

b. By definition, a function requires each input to have exactly one output. The input $3$ is paired with two different outputs ($7$ and $9$), so this is not a function.