vocabulary and concept check
1. vocabulary in an ordered pair, which number represents the input?
the output?
2. precision describe how relations and functions are different.
practice and problem solving
describe the pattern in the mapping diagram. copy and complete the diagram.
3. input output
1 → 4
2 → 8
3 → 12
4 → 20
5 → 26
6 → 32
4. input output
1 → 2
2 → 8
3 → 14
4 →
5 →
6 →
5. input output
1 → -3
2 → 2
3 → 7
4 →
5 →
6 →
list the ordered pairs shown in the mapping diagram.
6. input output
0 → 4
3 → 5
6 → 6
9 → 7
7. input output
1 → 8
3 → 6
3 → 4
5 → 6
5 → 4
7 → 2
8. input output
6 → -5
7 → -5
8 → -10
9 → -10
determine whether the relation is a function.
9. input output
-2 → 5
0 → 10
0 → 15
2 → 10
2 → 15
4 → 20
10. input output
0 → -18
4 → -9
8 → 0
12 → 9
11. input output
-3 → 7
-2 → 7
-1 → 14
0 → 14
12. error analysis describe and correct
the error in determining whether the
relation is a function.
(image of a mapping diagram with input 4 pointing to outputs 5, 6, 7, 8. text: each output
is paired w
exactly on
so, the r
is a fun)

Question

Accepted Answer

### Problem 6: List the ordered pairs shown in the mapping diagram.
# Explanation:
To list the ordered pairs, we take each input value and its corresponding output value. An ordered pair is in the form $(\text{input}, \text{output})$.

## Step 1: Identify input-output pairs
- For input $0$, output is $4$, so the ordered pair is $(0, 4)$.
- For input $3$, output is $5$, so the ordered pair is $(3, 5)$.
- For input $6$, output is $6$, so the ordered pair is $(6, 6)$.
- For input $9$, output is $7$, so the ordered pair is $(9, 7)$.

# Answer:
The ordered pairs are $(0, 4)$, $(3, 5)$, $(6, 6)$, $(9, 7)$.

### Problem 9: Determine whether the relation is a function.
# Explanation:
A relation is a function if each input has exactly one output. We check each input:

## Step 1: Check input $-2$
Input $-2$ maps to $10$ (only one output).

## Step 2: Check input $0$
Input $0$ maps to $10$ and $15$ (two outputs).

Since an input ($0$) has more than one output, the relation is not a function.

# Answer:
The relation is not a function because the input $0$ is paired with two outputs ($10$ and $15$).

### Problem 10: Determine whether the relation is a function.
# Explanation:
A relation is a function if each input has exactly one output. We check each input:

## Step 1: Check input $0$
Input $0$ maps to $-18$ (only one output).

## Step 2: Check input $4$
Input $4$ maps to $-9$ (only one output).

## Step 3: Check input $8$
Input $8$ maps to $0$ (only one output).

## Step 4: Check input $12$
Input $12$ maps to $9$ (only one output).

Each input has exactly one output, so the relation is a function.

# Answer:
The relation is a function because each input is paired with exactly one output.

### Problem 11: Determine whether the relation is a function.
# Explanation:
A relation is a function if each input has exactly one output. We check each input:

## Step 1: Check input $-3$
Input $-3$ maps to $7$ (only one output).

## Step 2: Check input $-2$
Input $-2$ maps to $7$ (only one output).

## Step 3: Check input $-1$
Input $-1$ maps to $14$ (only one output).

## Step 4: Check input $0$
Input $0$ maps to $14$ (only one output).

Each input has exactly one output (note: different inputs can map to the same output; the key is each input has one output), so the relation is a function.

# Answer:
The relation is a function because each input is paired with exactly one output.

### Problem 12: Error Analysis
# Explanation:
The error is in the reasoning about the definition of a function. A function requires that each **input** is paired with exactly one output, not each output with exactly one input. In the given diagram, the input $4$ is paired with multiple outputs ($5$, $6$, $7$, $8$), so the relation is not a function. The mistake was focusing on outputs instead of inputs.

To correct it: A relation is a function if each input has exactly one output. Here, the input $4$ is paired with four outputs, so the relation is not a function.

# Answer:
**Error Description**: The error is confusing the definition of a function. A function requires each input to have exactly one output, not each output to have exactly one input. The input $4$ is paired with multiple outputs ($5$, $6$, $7$, $8$).
**Correction**: Since the input $4$ has more than one output, the relation is not a function.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 6: List the ordered pairs shown in the mapping diagram.

Step 1: Identify input-output pairs

Step 1: Check input \(-2\)

Step 2: Check input \(0\)

Step 1: Check input \(0\)

Step 2: Check input \(4\)

Step 3: Check input \(8\)

Step 4: Check input \(12\)

Answer:

Problem 9: Determine whether the relation is a function.