Answer :
To fill in the table of values for the function [tex]\( y = 3x - 4 \)[/tex], we will evaluate the function at each given [tex]\( x \)[/tex] value and determine the corresponding [tex]\( y \)[/tex] values.
Let's go through this step-by-step:
1. For [tex]\( x = -3 \)[/tex]:
[tex]\[ y = 3(-3) - 4 = -9 - 4 = -13 \][/tex]
So, [tex]\( y = -13 \)[/tex].
2. For [tex]\( x = -1 \)[/tex] (already provided):
[tex]\[ y = -7 \][/tex]
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 3(1) - 4 = 3 - 4 = -1 \][/tex]
So, [tex]\( y = -1 \)[/tex].
4. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 3(3) - 4 = 9 - 4 = 5 \][/tex]
So, [tex]\( y = 5 \)[/tex].
5. For [tex]\( x = 5 \)[/tex]:
[tex]\[ y = 3(5) - 4 = 15 - 4 = 11 \][/tex]
So, [tex]\( y = 11 \)[/tex].
Now, let's fill in these values into the table:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ or $f(x)$ \\ \hline -3 & -13 \\ \hline -1 & -7 \\ \hline 1 & -1 \\ \hline 3 & 5 \\ \hline 5 & 11 \\ \hline \end{tabular} \][/tex]
So, the completed table is:
```
| x | y |
|----|----|
| -3 | -13|
| -1 | -7 |
| 1 | -1 |
| 3 | 5 |
| 5 | 11 |
```
These pairs [tex]\((-3, -13)\)[/tex], [tex]\((-1, -7)\)[/tex], [tex]\( (1, -1) \)[/tex], [tex]\( (3, 5) \)[/tex], and [tex]\( (5, 11) \)[/tex] are the points on the graph of the function [tex]\( y = 3x - 4 \)[/tex].
Let's go through this step-by-step:
1. For [tex]\( x = -3 \)[/tex]:
[tex]\[ y = 3(-3) - 4 = -9 - 4 = -13 \][/tex]
So, [tex]\( y = -13 \)[/tex].
2. For [tex]\( x = -1 \)[/tex] (already provided):
[tex]\[ y = -7 \][/tex]
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[ y = 3(1) - 4 = 3 - 4 = -1 \][/tex]
So, [tex]\( y = -1 \)[/tex].
4. For [tex]\( x = 3 \)[/tex]:
[tex]\[ y = 3(3) - 4 = 9 - 4 = 5 \][/tex]
So, [tex]\( y = 5 \)[/tex].
5. For [tex]\( x = 5 \)[/tex]:
[tex]\[ y = 3(5) - 4 = 15 - 4 = 11 \][/tex]
So, [tex]\( y = 11 \)[/tex].
Now, let's fill in these values into the table:
[tex]\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ or $f(x)$ \\ \hline -3 & -13 \\ \hline -1 & -7 \\ \hline 1 & -1 \\ \hline 3 & 5 \\ \hline 5 & 11 \\ \hline \end{tabular} \][/tex]
So, the completed table is:
```
| x | y |
|----|----|
| -3 | -13|
| -1 | -7 |
| 1 | -1 |
| 3 | 5 |
| 5 | 11 |
```
These pairs [tex]\((-3, -13)\)[/tex], [tex]\((-1, -7)\)[/tex], [tex]\( (1, -1) \)[/tex], [tex]\( (3, 5) \)[/tex], and [tex]\( (5, 11) \)[/tex] are the points on the graph of the function [tex]\( y = 3x - 4 \)[/tex].
