**Question:** Which is a table of ordered pairs defined by \( y = \dfrac{2}{7}x + 2 \)? **Answer Choices:** 1. \[ \begin{array}{c|c} x & f(x) \\ \hline -13 & -24 \\ 14 & 46 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 2. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 3. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & -24 \\ 21 & -4 \\ \end{array} \] **Explanation:** First, let’s rewrite the equation \( y = \dfrac{2}{7}x + 2 \) in function form: \( f(x) = \dfrac{2}{7}x + 2 \). To find the correct table of ordered pairs, substitute each \(x\) value from the tables into the function to see if \(f(x)\) equals the corresponding \(y\) value. For the first table: 1. For \( x = -13 \): \[ f(-13) = \dfrac{2}{7}(-13) + 2 = -\dfrac{26}{7} + 2 = -\dfrac{26}{7} + \dfrac{14}{7} = -\dfrac{12}{7} \approx -1.71 \neq -24 \] 2. For \( x = 14 \): \[ f(14) = \dfrac{2}{7}(14) + 2 = 4 + 2 = 6 \neq 46 \] 3. For \( x = -14 \): \[ f(-14) = \dfrac{2}{7}(-14) + 2 = -4 + 2 = -2 \neq 6 \] 4. For \( x = 21 \ The image displays two tables of values representing functions \( f(x) \) for different input values of \( x \). Here's the detailed transcription: ### Table 1 This table shows the values of \( f(x) \) for given \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 8 | 18 | | 14 | 18 | | -14 | 6 | | 21 | 46 | ### Table 2 This table presents another set of values of \( f(x) \) for different \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 15 | 32 | | 14 | -24 | | -14 | 6 | | 22 | -4 | Explanation: - Each table consists of two columns: one for the input value \( x \) and one for the corresponding output value \( f(x) \). - In the first table, the function \( f(x) \) maps: - \( x = 8 \) to \( f(x) = 18 \) - \( x = 14 \) to \( f(x) = 18 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 21 \) to \( f(x) = 46 \) - In the second table, the function \( f(x) \) maps: - \( x = 15 \) to \( f(x) = 32 \) - \( x = 14 \) to \( f(x) = -24 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 22 \) to \( f(x) = -4 \) These tables can be used to understand the different outputs of the same or different functions for various input values of \( x \).
**Question:** Which is a table of ordered pairs defined by \( y = \dfrac{2}{7}x + 2 \)? **Answer Choices:** 1. \[ \begin{array}{c|c} x & f(x) \\ \hline -13 & -24 \\ 14 & 46 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 2. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & 6 \\ 21 & -4 \\ \end{array} \] 3. \[ \begin{array}{c|c} x & f(x) \\ \hline 7 & 0 \\ 14 & -2 \\ -14 & -24 \\ 21 & -4 \\ \end{array} \] **Explanation:** First, let’s rewrite the equation \( y = \dfrac{2}{7}x + 2 \) in function form: \( f(x) = \dfrac{2}{7}x + 2 \). To find the correct table of ordered pairs, substitute each \(x\) value from the tables into the function to see if \(f(x)\) equals the corresponding \(y\) value. For the first table: 1. For \( x = -13 \): \[ f(-13) = \dfrac{2}{7}(-13) + 2 = -\dfrac{26}{7} + 2 = -\dfrac{26}{7} + \dfrac{14}{7} = -\dfrac{12}{7} \approx -1.71 \neq -24 \] 2. For \( x = 14 \): \[ f(14) = \dfrac{2}{7}(14) + 2 = 4 + 2 = 6 \neq 46 \] 3. For \( x = -14 \): \[ f(-14) = \dfrac{2}{7}(-14) + 2 = -4 + 2 = -2 \neq 6 \] 4. For \( x = 21 \ The image displays two tables of values representing functions \( f(x) \) for different input values of \( x \). Here's the detailed transcription: ### Table 1 This table shows the values of \( f(x) \) for given \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 8 | 18 | | 14 | 18 | | -14 | 6 | | 21 | 46 | ### Table 2 This table presents another set of values of \( f(x) \) for different \( x \) values: | \( x \) | \( f(x) \) | |:-------:|:---------:| | 15 | 32 | | 14 | -24 | | -14 | 6 | | 22 | -4 | Explanation: - Each table consists of two columns: one for the input value \( x \) and one for the corresponding output value \( f(x) \). - In the first table, the function \( f(x) \) maps: - \( x = 8 \) to \( f(x) = 18 \) - \( x = 14 \) to \( f(x) = 18 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 21 \) to \( f(x) = 46 \) - In the second table, the function \( f(x) \) maps: - \( x = 15 \) to \( f(x) = 32 \) - \( x = 14 \) to \( f(x) = -24 \) - \( x = -14 \) to \( f(x) = 6 \) - \( x = 22 \) to \( f(x) = -4 \) These tables can be used to understand the different outputs of the same or different functions for various input values of \( x \).
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Question:**
Which is a table of ordered pairs defined by \( y = \dfrac{2}{7}x + 2 \)?
**Answer Choices:**
1.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-13 & -24 \\
14 & 46 \\
-14 & 6 \\
21 & -4 \\
\end{array}
\]
2.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
7 & 0 \\
14 & -2 \\
-14 & 6 \\
21 & -4 \\
\end{array}
\]
3.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
7 & 0 \\
14 & -2 \\
-14 & -24 \\
21 & -4 \\
\end{array}
\]
**Explanation:**
First, let’s rewrite the equation \( y = \dfrac{2}{7}x + 2 \) in function form: \( f(x) = \dfrac{2}{7}x + 2 \).
To find the correct table of ordered pairs, substitute each \(x\) value from the tables into the function to see if \(f(x)\) equals the corresponding \(y\) value.
For the first table:
1. For \( x = -13 \):
\[
f(-13) = \dfrac{2}{7}(-13) + 2 = -\dfrac{26}{7} + 2 = -\dfrac{26}{7} + \dfrac{14}{7} = -\dfrac{12}{7} \approx -1.71 \neq -24
\]
2. For \( x = 14 \):
\[
f(14) = \dfrac{2}{7}(14) + 2 = 4 + 2 = 6 \neq 46
\]
3. For \( x = -14 \):
\[
f(-14) = \dfrac{2}{7}(-14) + 2 = -4 + 2 = -2 \neq 6
\]
4. For \( x = 21 \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5008f26-46d2-4d82-9842-753838f38708%2Fcb90a7c4-be0e-4b9d-bf81-e63bfa474bb9%2Fum1py4b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which is a table of ordered pairs defined by \( y = \dfrac{2}{7}x + 2 \)?
**Answer Choices:**
1.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
-13 & -24 \\
14 & 46 \\
-14 & 6 \\
21 & -4 \\
\end{array}
\]
2.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
7 & 0 \\
14 & -2 \\
-14 & 6 \\
21 & -4 \\
\end{array}
\]
3.
\[
\begin{array}{c|c}
x & f(x) \\
\hline
7 & 0 \\
14 & -2 \\
-14 & -24 \\
21 & -4 \\
\end{array}
\]
**Explanation:**
First, let’s rewrite the equation \( y = \dfrac{2}{7}x + 2 \) in function form: \( f(x) = \dfrac{2}{7}x + 2 \).
To find the correct table of ordered pairs, substitute each \(x\) value from the tables into the function to see if \(f(x)\) equals the corresponding \(y\) value.
For the first table:
1. For \( x = -13 \):
\[
f(-13) = \dfrac{2}{7}(-13) + 2 = -\dfrac{26}{7} + 2 = -\dfrac{26}{7} + \dfrac{14}{7} = -\dfrac{12}{7} \approx -1.71 \neq -24
\]
2. For \( x = 14 \):
\[
f(14) = \dfrac{2}{7}(14) + 2 = 4 + 2 = 6 \neq 46
\]
3. For \( x = -14 \):
\[
f(-14) = \dfrac{2}{7}(-14) + 2 = -4 + 2 = -2 \neq 6
\]
4. For \( x = 21 \
Transcribed Image Text:The image displays two tables of values representing functions \( f(x) \) for different input values of \( x \). Here's the detailed transcription:
### Table 1
This table shows the values of \( f(x) \) for given \( x \) values:
| \( x \) | \( f(x) \) |
|:-------:|:---------:|
| 8 | 18 |
| 14 | 18 |
| -14 | 6 |
| 21 | 46 |
### Table 2
This table presents another set of values of \( f(x) \) for different \( x \) values:
| \( x \) | \( f(x) \) |
|:-------:|:---------:|
| 15 | 32 |
| 14 | -24 |
| -14 | 6 |
| 22 | -4 |
Explanation:
- Each table consists of two columns: one for the input value \( x \) and one for the corresponding output value \( f(x) \).
- In the first table, the function \( f(x) \) maps:
- \( x = 8 \) to \( f(x) = 18 \)
- \( x = 14 \) to \( f(x) = 18 \)
- \( x = -14 \) to \( f(x) = 6 \)
- \( x = 21 \) to \( f(x) = 46 \)
- In the second table, the function \( f(x) \) maps:
- \( x = 15 \) to \( f(x) = 32 \)
- \( x = 14 \) to \( f(x) = -24 \)
- \( x = -14 \) to \( f(x) = 6 \)
- \( x = 22 \) to \( f(x) = -4 \)
These tables can be used to understand the different outputs of the same or different functions for various input values of \( x \).
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