Graph your Driving

For each part below, sketch the graph or graphs as indicated. Note: Your homework solution graphs must be fully labelled and please include the the wording of the full question (you can copy and paste from I. through V. below) above each of your graphs. use graph paper (or else use a ruler to carefully draw as accurately as possible).

  1. Suppose your annual driving mileage is 12,000 miles per year. Suppose your car car's Fuel Economy is 25 miles per gallon (mpg) for the average of a year's worth of (local and highway) driving. Draw a graph of your annual gas cost in dollars (the "y-axis" or "dependent" variable) as a function of the cost of gas (in $/gallon), the latter being your "x-axis" or "independent" variable.

    Labeling: 1. Label your graph by an equation, 2. show all the preceding work that led to this equation, and 3 label your x-axis and y-axis numerically (marking notches for $2/gallon, $2.50/gallon, $3/gallon and $3.5/gallon for example) as well as 4. labeling them with words (e.g. "annual gas cost") and 5. with the variable (e.g. "C" if you use "C" for cost in your equation)

  2. In this scenario, suppose gas costs exactly $3/gallon. You will draw four graphs (note: you will want to draw a large, e.g. ½ page or almost as large, so all four graphs will be easily visible) on a single st of x- and y-axis coordinates:
    1. In the first case, assume your car's fuel economy is 10 mpg (Hummer?)
    2. In the first case, assume your car's fuel economy is 20 mpg (Typical car?)
    3. In the first case, assume your car's fuel economy is 30 mpg (Compact/Economy)
    4. In the first case, assume your car's fuel economy is 60 mpg (Advanced Hybrid?)

    In each case, you will graph "annual cost" (your y-axis variable) as a function of how many miles you choose to (or have to) travel per year.

    See the above paragraph for part I. regarding making sure you including all five parts of the "Show steps" and "labeling" required, in order to receive full credit

  3. This time, continue to assume that gas costs exactly $3/gallon, but assume that your budget only allows you to spend $1,500 per year on gasoline. Graph how many miles you will be able to travel per year (the dependent or y-axis variable) as a function of the mpg fuel economy your car has (the independent variable). First plot individual points corresponding to the following cases: mpg ratings of 10, 20, 30, 40, 50, and 60 miles per gallon, respective; then sketch a curve for the entire graph.

    See the above paragraph for part I. regarding making sure you including all five parts of the "Show steps" and "labeling" required in order to receive full credit

  4. Now we are back to not having to stay within a budget: assume your annual driving is 12,000 miles for year, and that gas, still costs $3/gallon exactly. How much money gas will cost you for the year, as a function of your car's MPG rating.

    First plot points corresponding to 10, 15, 20, 25, 30, 40, 50, and 60 miles per gallon (mpg), and then sketch a curve for the entire graph.
    See the above paragraph..regarding... [etc...in order to get full credit!]

  5. Finally, Assume you are back to a budget: this time your budget is $2,000 for how much you can spend on gas for the year; and assume your car's fuel economy is 25 miles per gallon. Sketch a graph for the number of miles per year you will be able to travel, as a function of the cost of gas, in dollars per gallon.
    See the above paragraph..regarding... [etc...in order to get full credit!]