Answer the questions on your own paper first, or use your notes.

Jermaine plays basketball for Americanville High. During this season, he has made eight out of 14 free throws. If he makes every one of his free throws from now until the end of the season, his percentage could be found using the equation:

y = 8 + x 14 + x

where y is the percentage and x is the number of free throws he attempts and makes from now on.

  1. What is Jermaine's percentage as of now? Where is this point located on the graph?
    2. Interactive popup. Assistance may be required.

    Check Your Answer

    Answer: 57%; the y-intercept

    Right now, Jermaine has made 8 out of 14 free throws. That is 57%. As for the graph, right now Jermaine has thrown zero more free throws so x = 0. The y-intercept is the value of y when x = 0.

    Close Pop Up
  2. Use the graph of the function to determine Jermaine's percentage if he throws and makes 10 more free throws this season.

    Interactive popup. Assistance may be required.

    Check Your Answer

    Answer: 75%. Enter the equation into your graphing calculator. Be sure to group the numerator and group the denominator.

    Three screen shots from a graphing calculator: 1. displays the equation y equals (8+x)/(14+X). 2. displays the X and Y max and min values for the graphing window. 3. displays the graph of the equation with a dot at x = 10, y = 7.5 Close Pop Up

  3. How many more free throws would Jermaine need to make for his percentage to be 90%?
    4. Interactive popup. Assistance may be required.

    Check Your Answer

    Answer: 46.
    Equation box and two screen shots from a graphing calculator: 1. Steps used to solve the equation 0.90=(8+x)/(14+x). 2. Screen shot displays the X and Y values from a graphing calculator output. X=46, Y1=.9 is highlighted. 3. Screen shot displays the graph of the equation with a dot at x=46, y=.9 Close Pop Up
  4. Can Jermaine ever have a free throw percentage of 100%? If so, how many free throws must he throw and make? If not, explain why not. How is this fact represented on the graph?
    5. Interactive popup. Assistance may be required.

    Check You Answer

    No, Jermaine can never have a free throw percentage of 100%. 100% means he made every free throw. There are already 6 free throws that he did not make. It is the horizontal asymptote that represents this fact on the graph. The graph of the function curves ever closer to y = 1 (which is y = 100%) but never actually has a point where y = 1.

    Close Pop Up
  5. How many free throws would Jermaine need to make for his average to be 99.9%? Is this reasonable?
    6. Interactive popup. Assistance may be required.

    Check Your Answer

    Jermaine would need to make 5956 more free throws for his average to be 99.9%. This number of free throws is definitely unreasonable for one season. According to NBA Regular Season Records, Karl Malone has the most free throws in a career (9,787). Jerry West has the most free throws in one season (840). These men are professionals; Jermaine is not.

    1 box and 2 screen shots from a graphing calculator: 1. box contains steps used to solve the equation 0.99=(8+x)/(14+x). 2. screen shot displays the graph of the equation with the intersection x=5986, y=.999. 3. screen shot displays the X and Y values from a graphing calculator output. X=5957, Y1=.999 is highlighted. Close Pop Up
  6. What is a reasonable domain for this situation?
    7. Interactive popup. Assistance may be required.

    Check Your Answer

    0 to number of free throw opportunities this season minus the 8 Jermaine already has.

    If we use the above statistic then the domain would be 0 ≤ x ≤ 832-ish

    It would also be reasonable to use a number significantly smaller than 832.

    Close Pop Up
  7. What is a reasonable range?
    8. Interactive popup. Assistance may be required.

    Check Your Answer

    57% ≤ y < 100%

    Jermaine starts with a 57% free throw percentage but he cannot attain 100%.

    Close Pop Up