At Ontario Tech University, the final grade a student earns in the course corresponds to a letter grade. Is the letter grade a function of the percentage a student can obtain in th... At Ontario Tech University, the final grade a student earns in the course corresponds to a letter grade. Is the letter grade a function of the percentage a student can obtain in the course? Is the percentage a student can obtain in the course a function of the letter grade? Justify. Consider information related to bank accounts: a) Is the account balance a function of the bank account number? Justify. b) Is the bank account number a function of the account balance? Justify. Introduce function notation of your choice using variable names to represent a function that takes as input the name of a month, and gives as output the number of days in that month. State clearly what each variable represents. A Function N(y) gives the number of police officers, N, in a town in year y. What does N(2005) = 300 tell us? Which of these tables define a function (if any)? Justify. Using the table for Q(n): Evaluate Q(3) and interpret your result (describe in words what the answer means). Solve Q(n) = 6 and interpret your result. Evaluate Q(7). Interpret your result. Solve Q(n) = 1. Interpret your result. Read more

Steps to Solve

1. Analyze Price and Item Relationship

   To determine if price is a function of the item, we consider whether each item has a unique price. Since each item on the menu corresponds to exactly one price, we can conclude that price is a function of the item.

2. Evaluate Grades and Percentages

   We need to check:

   • If the letter grade is a function of the percentage. Each percentage corresponds to one unique letter grade based on the grading scale, so yes, it is a function.
   • Whether the percentage is a function of the letter grade. One letter grade corresponds to multiple percentages (e.g., C can range from 60% to 69%). Therefore, the percentage is not a function of the letter grade.

3. Bank Accounts Relationship Analysis

   (a) The account balance is a function of the bank account number because each account number corresponds to one unique balance.

   (b) The bank account number is not a function of the account balance because a single balance can be associated with multiple account numbers.

4. Function Notation Example

   Define a function ( D(m) ) where ( m ) represents the month (e.g., January = 1, February = 2). The output will be the number of days in that month. For example:

   • ( D(1) = 31 ) (January)
   • ( D(2) = 28 ) or ( D(2) = 29 ) (February, depending on the year)

5. Understanding Function N(y)

   ( N(y) ) indicates the number of police officers in a town for year ( y ). ( N(2005) = 300 ) tells us that there were 300 police officers in the year 2005.

6. Evaluating Tables for Function Definition

   Table analysis:

   • Table a):
     • Input: (2 \rightarrow 1), (5 \rightarrow 3), (8 \rightarrow 6) (all inputs unique).
   • Table b):
     • Input: (-3 \rightarrow 5), (0 \rightarrow 1), (4 \rightarrow 5) (the output (5) is repeated for two inputs, not a function).
   • Table c):
     • Input: (1 \rightarrow 0), (5 \rightarrow 2), (5 \rightarrow 4) (the input (5) corresponds to two outputs, not a function).

7. Evaluate Q(n) and Interpret Results

   a) Evaluate ( Q(3) ):

   • From the table, ( Q(3) = 7 ). This means that when ( n = 3 ), the quantity ( Q ) is 7.

   b) Solve ( Q(n) = 6 ):

   • Looking at the table, ( n = 4 ) when ( Q(n) = 6 ). This means if the quantity is 6, it corresponds to the input ( n = 4 ).

   c) Evaluate ( Q(7) ):

   • The table shows ( Q(7) ) is not present, thus undefined.

   d) Solve ( Q(n) = 1 ):

   • From the table, ( n = 0 ) corresponds to ( Q(n) = 1 ).