Linear Applications

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Good Graph vs. Bad Graph – Part 2 – Linear Applications

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.

Bad Graph - Linear Applications

Good Graph - Linear Applications


Checklist for a Good Graph – Linear Applications

  1. Label the horizontal and vertical axes with the problem variables.
  2. Identify tick marks. In this graph, every two tick marks are a distance of 1 (horizontal) or 100 (vertical).
  3. 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.
  4. 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.