# mapping diagram, algebra homework

**Question description**

- Below, you are given a mapping diagram.
- Create and justify a relation that represents a function with the given range. Write your answers as ordered pairs.
- Create and justify a relation that does not represent a function with the given range. Write your answers as ordered pairs.

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

- Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
- f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
- f(n) = 35n
- Which one of these formulas show the sequence written recursively, and which shows it written explicitly? Justify your explanations.
- Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means.
- Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations.
- 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.

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

- 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.

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