Mapping diagram

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  1. Below, you are given a mapping diagram.
    Image of domain bubble and range bubble. Inside the range bubble, the numbers 11, 20, 34, and 41 appear.

    1. Create and justify a relation that represents a function with the given range. Write your answers as ordered pairs.
    2. Create and justify a relation that does not represent a function with the given range. Write your answers as ordered pairs.

     
  2. Find the equation of the line in the graph, and mathematically model the scenario using function notation where cost is a function of number of minutes. 
    cell phone plan graph : Line starting at (0, 20) and going through 400, 40
  3. A textbook company keeps track of its daily cost for printing whole textbooks to different schools, but can only print up to 500 books a day. The daily cost (C) to print x number of textbooks is given by C(x) = 3.50x + 1200. 

    1. Using the function, determine one possible daily cost by evaluating the function for any input of your choice.
    2. For what value of x does C(x) = 1900?
    3. Interpret the statement C(20) = 1270.
    4. Interpret the statement C(w) = p.
    5. Explain whether C(40.5) = 1341.75 is correct and possible given the context of this problem.

     
  4. Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
    1. f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
    2. f(n) = 35n
      1. Which one of these formulas show the sequence written recursively, and which shows it written explicitly? Justify your explanations.
      2. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.
      3. Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.
      4. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.

     
  5. Create your own equation written in standard form.
    1. Determine any point that is a solution and will be on this line. Justify your answer algebraically.
    2. Explain how to find the x- and y- intercepts using complete sentences. Write the intercepts as ordered pairs.
    3. Rewrite the equation using function notation. Graph the function and show the intercepts.

     
  6. Compare the graph from question 2 and the equation from question 5. How are the graphs similar and different? Determine which has the greater y-value when x is 160, and explain how you determined it.
    • 7 years ago
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