Suppose you purchase a washing machine for $500 and it depreciates $100 a year. If t represents time in years then the function V(t) = -100t + 500 represents the value of your machine over time.
This function has a restricted domain (usually called a PRACTICAL DOMAIN) because there are limits on what the input can be. The inputs can start at 0 (the year you purchased the machine) and go to 5 (because at 5 years the machine is worth $0). So, in mathematical language, we say that 0 ≤ t ≤ 5 is the practical domain of function V(t).
The function also has a restricted range (usually called a PRACTICAL RANGE) and it is closely related to the restricted domain. If t = 0, then V(0) = 500 which is the purchase price of the washer (i.e. the initial value). If t = 5, then V(5) = 0 which is the value of the washer after 5 years. So, in mathematical language, we say that 0 ≤ V(t) ≤ 500 is the practical range of the function V(t). [Notice that we list the numbers for the range in numerical order even though the biggest one, 500, is the first one we discovered].
Now let’s look at a couple of graphs for V(t). The first one is a bad graph and the second one is a good graph. Below the second graph is a checklist of items to include when creating a good graph for linear applications. There are some important differences between a good graph for linear applications and a good graph for linear equations. Compare the checklist here to the checklist in Part 1 to be sure you understand what those differences are.
Checklist for a Good Graph – Linear Applications
- Label the horizontal and vertical axes with the problem variables.
- Identify tick marks. In this graph, every two tick marks are a distance of 1 (horizontal) or 100 (vertical).
- Plot and label at least two ordered pairs from the function. The most common points to plot for applications of this type are the vertical and horizontal intercepts.
- Use a straightedge to connect the plotted points and DO NOT run the line past the starting and ending points. Applications usually involve a restricted domain and the plotted beginning and end points are the first and last points on the graph.