Question

A magician charges $50.00 for a visit and an additional $7.50 for each hour he performs. The function rule C = 7.50h + 50.00 describes the
relationship between the number of hours h and the total cost of the visit C. If the magician will only visit a maximum of 8 hours, what is a reasonable graph of the function rule?

Answer 1

To create a graph for the given function rule C = 7.50h + 50.00, we need to plot the total cost of the visit C on the y-axis and the number of hours h on the x-axis.

Since the magician will only visit a maximum of 8 hours, we can create a table with values for h from 0 to 8.

h | C = 7.50h + 50.00
-------------------
0 | 50.00
1 | 57.50
2 | 65.00
3 | 72.50
4 | 80.00
5 | 87.50
6 | 95.00
7 | 102.50
8 | 110.00

Plotting these points on the graph, we get:

(Note: The scale of the graph may vary depending on the available space)

```
|
120+
| *
110+ *
| |
100+ |
| |
90+ |
| |
80+ |
| |
70+ |
| |
60+ |
| |
50+---*---*---*---*---*---*---*---*---* (h)
0 1 2 3 4 5 6 7 8
```

This graph shows a reasonable representation of the function rule. The initial cost of $50.00 is represented by the y-intercept (0, 50.00), and the slope of 7.50 represents the additional cost per hour. As the number of hours increases, the total cost of the visit increases linearly.