A. Let's first complete the table by calculating the total cost for each number of cartridges from 0 to 4. The equation provided is [tex]\( y = 15x + 80 \)[/tex].
Given:
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = 15 \times 0 + 80 = 80 \)[/tex]
- When [tex]\( x = 1 \)[/tex]: [tex]\( y = 15 \times 1 + 80 = 95 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = 15 \times 2 + 80 = 110 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( y = 15 \times 3 + 80 = 125 \)[/tex]
- When [tex]\( x = 4 \)[/tex]: [tex]\( y = 15 \times 4 + 80 = 140 \)[/tex]
Let's fill in the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
\begin{tabular}{l}
Number of \\
cartridges, $x$
\end{tabular}
&
\begin{tabular}{l}
Cost, $y$ \\
(dollars)
\end{tabular}
\\
\hline
0 & 80 \\
\hline
1 & 95 \\
\hline
2 & 110 \\
\hline
3 & 125 \\
\hline
4 & 140 \\
\hline
\end{tabular}
\][/tex]
Now, let's summarize the domain and range:
Domain: [tex]\( \{0, 1, 2, 3, 4\} \)[/tex]
Range: [tex]\( \{80, 95, 110, 125, 140\} \)[/tex]
B. To graph the points from Part A, we plot the pairs [tex]\((x, y)\)[/tex]:
- [tex]\((0, 80)\)[/tex]
- [tex]\((1, 95)\)[/tex]
- [tex]\((2, 110)\)[/tex]
- [tex]\((3, 125)\)[/tex]
- [tex]\((4, 140)\)[/tex]
Here is a sketch of the graph:
```
Cost (y)
|
|
| (4, 140)
|
|
|
| (0, 80)
|
|______________________
0 1 2 3 4 (x)
Number of cartridges
```
On the x-axis, we have the number of cartridges, and on the y-axis, we have the cost in dollars. Each point represents the total cost for a given number of cartridges as calculated above.
