Jeff builds model train layouts. He has $75 to spend on packages of miniature landscape items. He receives 6 free packages with each other. The number of packages that Jeff can buy is given by y = 75/x + 6, where x represents the cost of each package in dollars. Describe the reasonable domain and range value and graph the function.

plot it the way you plot any function! Pick some values of x and calculate y. Then plot the point at (x,y).

The curve will be smooth, but the only poi9nts that make sense in the real world are where x is a divisor of 75.

Your graph should look like this:

http://www.wolframalpha.com/input/?i=plot+75%2Fx%2B6+for+x%3D1..20

To find the reasonable domain and range value for the given function y = 75/x + 6, we need to consider the restrictions imposed by the context of the problem.

Domain:
In this case, the domain represents the possible values for x, which is the cost of each package in dollars. However, since we cannot have negative values for the cost of a package, the domain must be limited to x > 0. This means that the cost of each package must be a positive number.

Range:
The range represents the possible values for y, which in this case represents the number of packages that Jeff can buy. Since the number of packages cannot be negative, the range must be limited to y > 0.

Graph:
To graph the given function, we can start by choosing different values for x and finding the corresponding values for y. Here is a table of values:

x | y
-------
1 | 81
5 | 21
10 | 13.5
15 | 11
20 | 9.75

Now, we can plot these points on a graph and connect them to get the graph of the function y = 75/x + 6.

(Note: The scale of the graph may vary, so it's important to label the axes accordingly.)

From the graph, we can observe that as the cost of each package (x) increases, the number of packages Jeff can buy (y) decreases. This relationship makes sense because as the cost per package increases, Jeff's budget of $75 will allow him to buy fewer packages.

The graph also shows that the function is undefined at x = 0 since we cannot have a package with a cost of zero.

Therefore, the reasonable domain for this function is x > 0, and the range is y > 0.

I hope this helps in understanding the concept and solving the problem!