In math, verbal descriptions of the functions describing a problem situation are sometimes used instead of a mathematical equation.

For example

Maria just purchased a new compact car with hopes to save money driving to work and back. Maria tracked her expenses for six months in order to determine the average monthly cost of operating her new car. In addition to the cost of gas (the cost of gas is $4 per gallon), Maria calculated a monthly fee of $120 that includes maintenance and insurance costs.

1. What is the cost that is constant each month?
   
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   Each month there is a constant fee of $120 for car maintenance and insurance.
2. Below is a graph of the above function. Press the animate button to move the car along the horizontal axis and, view the graph.
   
   
   
   In your notes or on your own piece of paper, describe the function as the car moves across the horizontal axis. In your description, state what is changing (the independent and dependent variable) and the type of function (linear or quadratic). If the function is linear, state if the slope is positive or negative.
   
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   The independent variable, or the horizontal axis, is the number of miles Maria drove. The dependent variable, or the vertical axis, is the total cost of operating the vehicle. It is a linear function in the first quadrant with a positive slope of 4.
3. Move the car along the horizontal axis below to view another graph of Maria's cost to drive her car.
   
   
   
   
   Describe the graph and give a possible explanation for the graph.
   
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   The constant value is $120 for the cost of insurance, the independent variable is the number of miles driven, and the slope of the linear function is zero. The dependent variable is the constant, $120. Since the slope is zero there isn't a cost for gas. One possible explanation would be Maria is in a carpool where the others pay her to drive. The income she collects pays for the gas for her car.
4. Describe the difference between the two graphs.
   
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   The slope is different between the two graphs. The first graph has a slope of 4 while the second graph has a slope of zero.