Technology, Math, Education

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.

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Below are examples of a GOOD graph for the linear equation y = 2x + 4 and a BAD graph for the linear equation y = 2x + 4. At the end of the post is a checklist that you can use to be sure you are creating GOOD graphs for all your linear equations.

Checklist for a good graph – Linear Equations

- Label the horizontal and vertical axes with the appropriate symbols.
- Identify tick marks (in this case distance is 10 in each direction from the origin).
- Plot and label at least two ordered pairs that are on the graph of the equation. If you have a third point, plot and label it just for checking purposes.
- Use a straightedge to connect the points and run the graph through and beyond the end points (unless the domain is restricted).

Note: The lack of closed endpoints on the graph indicates that it continues forever in each direction.

If you are trying to graph on your TI83/84 and you get the INVALID DIM error, then this usually means your PLOT is turned on. Follow the steps below to turn off your PLOT and see if the problem is fixed.

Here is what your screen looks like with the error:

From THIS screen, follow these key strokes exactly to turn off your PLOT:

Your Y= area should now look like this:

Whereas before, it looked like this:

A good rule of thumb is, anytime you are using the STATPLOT, be sure to turn OFF your PLOT when you are finished. That way you will avoid the INVALID DIM Error in the future.

Related Post: Turn PLOT on

Couldn’t resist including this graph on the site. It’s not my creation…just one I wish I had created. The original author is someone named Peter Vidani. You can visit his site and see the original graph and the Creative Commons copyright information. Please be kind and share his info if you decide to use this graphic…share and share alike.