Example 3 in many classes the overall percentage you

Example 3
In many classes the overall percentage you earn in the course corresponds to a decimal
grade point. Is decimal grade a function of percentage? Is percentage a function of
decimal grade?
For any percentage earned, there would be a decimal grade associated, so we could say
that the decimal grade is a function of percentage. That is, if you input the percentage,
your output would be a decimal grade. Percentage may or may not be a function of
decimal grade, depending upon the teacher’s grading scheme. With some grading
systems, there are a range of percentages that correspond to the same decimal grade.
One-to-One Function
Sometimes in a relationship each input corresponds to exactly one output, and every
output corresponds to exactly one input. We call this kind of relationship a one-to-one
function .
From Example 3, if each unique percentage corresponds to one unique decimal grade
point and each unique decimal grade point corresponds to one unique percentage then it
is a one-to-one function.
Try it Now
Let’s consider bank account information.
1. Is your balance a function of your bank account number?
(if you input a bank account number does it make sense that the output is your balance?)
2. Is your bank account number a function of your balance?
(if you input a balance does it make sense that the output is your bank account number?)
Function Notation
To simplify writing out expressions and equations involving functions, a simplified
notation is often used. We also use descriptive variables to help us remember the
meaning of the quantities in the problem.
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Section 1.1 Functions and Function Notation 3
Rather than write “height is a function of age”, we could use the descriptive variable h to
represent height and we could use the descriptive variable a to represent age.
“height is a function of age” if we name the function f we write
“ h is f of a ” or more simply
h = f(a) we could instead name the function h and write
h(a) which is read “ h of a ”
Remember we can use any variable to name the function; the notation h(a) shows us that
h depends on a . The value “ a ” must be put into the function “ h ” to get a result. Be
careful - the parentheses indicate that age is input into the function (Note: do not confuse
these parentheses with multiplication!).
Function Notation
The notation output = f (input) defines a function named f . This would be read “output
is f of input”
Example 4
Introduce function notation to represent a function that takes as input the name of a
month, and gives as output the number of days in that month.
The number of days in a month is a function of the name of the month, so if we name
the function f , we could write “days = f (month)” or d = f(m) . If we simply name the
function d , we could write d(m)
For example, d (March) = 31, since March has 31 days. The notation d(m) reminds us
that the number of days, d (the output) is dependent on the name of the month, m (the
input)
Example 5
A function N = f(y) gives the number of police officers, N , in a town in year y . What
does f (2005) = 300 tell us?