unit 2: sequences review
1. state whether the relation is a function or not a function.
a. {(-7,1),(3, - 8),(-3,2),(-7,5)}
b. {(2,5),(4,6),(8,3),(-1,6)}
c. domain: {1,4,-2,5,6,7} range: {3,1,-5,6,2,9}
d.
|x|y|
|-2|2|
|-1|4|
|0|3|
|1|6|
|2|4|
e.
2. express the relationship as a table, as a graph, and as a mapping. also, state the domain, range, and if the relation is a function. {(-3,4),(2,5),(3,2),(0,3),(-1,2)}
table
|x|y|
| | |
mapping
graph
what is the domain?
what is the range?
is it a function? how do you know?
3. fill in the table and graph for the dot pattern below. you only need to graph figures #1 through #6.
|figure #|figure #|figure #|# of dots|
|1|||
|2|||
|3|||
|4|||
|5|||
|6|||
| - |||
|20|||
|n|||
circle one: geometric or arithmetic

Question

Accepted Answer

### 1.
- **a. $\{(-7,1),(3, - 8),(-3,2),(-7,5)\}$**
  - **Explanation**:
    - **Step 1: Recall function - definition**
A function is a relation where each input (x - value) has exactly one output (y - value). In the given relation, the input $x=-7$ has two outputs $y = 1$ and $y = 5$.
  - **Answer**: Not a function.
- **b. $\{(2,5),(4,6),(8,3),(-1,6)\}$**
  - **Explanation**:
    - **Step 1: Check for unique inputs**
Each x - value $2$, $4$, $8$, and $-1$ has a single corresponding y - value.
  - **Answer**: A function.
- **c. Given domain $\{1,4,-2,5,4,7\}$ and range $\{3,1, - 5,6,2,9\}$**
  - **Explanation**:
    - **Step 1: Analyze domain for duplicates**
The input $x = 4$ appears twice in the domain. Since we don't know the exact pairings, but the presence of a repeated input in the domain without information that it maps to the same output means we can't be sure it's a function. In a more strict sense, if we assume that a relation is defined by the domain - range pairs, a repeated input in the domain without a single - valued output violates the function definition.
  - **Answer**: Not a function (assuming non - single - valued output for repeated input).
- **d. The table $\begin{array}{|c|c|}\hline x&y\\hline - 2&2\\hline - 1&4\\hline0&3\\hline1&6\\hline2&4\\hline\end{array}$**
  - **Explanation**:
    - **Step 1: Check x - values for uniqueness**
Each x - value $-2$, $-1$, $0$, $1$, and $2$ has exactly one y - value associated with it.
  - **Answer**: A function.
- **e. The mapping diagram**
  - **Explanation**:
    - **Step 1: Check for one - to - one or many - to - one mapping**
The input $-7$ maps to two different outputs ($-3$ and $9$).
  - **Answer**: Not a function.
- **f. The graph (not shown in detail here, but assuming a standard vertical - line test approach)**
  - **Explanation**:
    - **Step 1: Apply vertical - line test**
If a vertical line can be drawn such that it intersects the graph at more than one point, the relation is not a function. Without seeing the graph, if there are multiple y - values for a single x - value, it's not a function.

### 2. For the relation $\{(-3,4),(2,5),(3,2),(0,3),(-1,2)\}$
- **Table**:
  - **Explanation**:
    - **Step 1: Organize x and y values**
$\begin{array}{|c|c|}\hline x&y\\hline - 3&4\\hline - 1&2\\hline0&3\\hline2&5\\hline3&2\\hline\end{array}$
- **Mapping**:
  - **Explanation**:
    - **Step 1: Draw two ovals for domain and range**
One oval for the domain $\{-3,-1,0,2,3\}$ and another for the range $\{2,3,4,5\}$. Then draw arrows from each x - value in the domain oval to its corresponding y - value in the range oval.
- **Graph**:
  - **Explanation**:
    - **Step 1: Plot points**
Plot the points $(-3,4)$, $(-1,2)$, $(0,3)$, $(2,5)$, and $(3,2)$ on the coordinate plane.
- **Domain**:
  - **Explanation**:
    - **Step 1: List x - values**
The set of all x - values in the relation is $\{-3,-1,0,2,3\}$.
  - **Answer**: $\{-3,-1,0,2,3\}$
- **Range**:
  - **Explanation**:
    - **Step 1: List y - values**
The set of all y - values in the relation is $\{2,3,4,5\}$.
  - **Answer**: $\{2,3,4,5\}$
- **Function or not**:
  - **Explanation**:
    - **Step 1: Check for unique x - values**
Each x - value has exactly one y - value associated with it.
  - **Answer**: A function.

### 3.
- **The dot - pattern**:
  - **Table**:
    - We observe that the number of dots in figure $n$ forms a pattern. The number of dots in figure $1$ is $2$, in figure $2$ is $4$, in figure $3$ is $6$, in figure $4$ is $8$, in figure $5$ is $10$, in figure $6$ is $12$, in figure $20$ is $40$, and in general, for figure $n$ is $2n$.
    - $\begin{array}{|c|c|}\hline\text{Figure \#}&\text{\# of Dots}\\hline1&2\\hline2&4\\hline3&6\\hline4&8\\hline5&10\\hline6&12\\hline20&40\\hline n&2n\\hline\end{array}$
  - **Graph**:
    - **Explanation**:
      - **Step 1: Set up axes**
Let the x - axis represent the figure number $n$ and the y - axis represent the number of dots.
      - **Step 2: Plot points**
Plot the points $(1,2)$, $(2,4)$, $(3,6)$, $(4,8)$, $(5,10)$, $(6,12)$ on the coordinate plane.
    - **Type of sequence**:
      - **Explanation**:
        - **Step 1: Check for common difference**
The difference between consecutive number of dots: $4 - 2=2$, $6 - 4 = 2$, $8 - 6=2$, etc. Since there is a common difference of $2$ between consecutive terms, it is an arithmetic sequence.
      - **Answer**: Arithmetic.

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QUESTION IMAGE

Question

Explanation:

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2. For the relation \(\{(-3,4),(2,5),(3,2),(0,3),(-1,2)\}\)

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Answer:

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2. For the relation \(\{(-3,4),(2,5),(3,2),(0,3),(-1,2)\}\)

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