Function Notation
WHAT IS IT ALL ABOUT?
Function Notation
 f(x) is used as a “fancy” notation for functions.
Example 1:
y = 2x + 3
same as … f(x) = 2x + 3
Function Notation
f(x) is used as a “fancy” notation for functions.
Example 2:
y = -3x + 1
same as …. g(x) = -3x + 1
How to read function Notation?
f(x) = 2x + 3

Read as …..
“f of x equals 2 times “x” plus 3”
Function Notation
g(x) = -2x – 1

Read as ….
“g of x equals -2 times “x” minus 1”
Function Notation Approach
 Why Function Notation?
 It allows for more flexibility!
Example:
 Both functions have a unique rule that “depends” on
the size of the radius (r ).
Function Practice
Example 1:
f(x) = -2x + 4
 Evaluate for x = 3
f(3) = -2(3) + 4
 replace x with “3”.
f(3) = -2
 Our final result/answer
Evaluate Function Notation
Example 2:
f(x) = -2x + 4
 Evaluate for x = 5
f(5) = -2(5) + 4 = -6
 replace x with “5”.
f(5) = -6
 Our final result/answer
Evaluate Function Notation
Example 3:
For f(x) = -2x + 4
f(a) = -2a + 4
 Evaluate for x = a
 replace x with “a”
f(a) = -2a + 4  answer is an expression
Real Life Examples
 Phone bill (t) = $0.05(t) + $14.95
Where t = time in minutes
 The amount you pay is based on how many minutes
you talk.
Real Life Example
 grade(t) = 10t + 60
Where t = the number of hours you study.
 Your grade is a function of the amount of time you
study!
Sample Problem
You try a few examples:
 For f(x) = -2x + 4
Evaluate
f(2) = ?
Sample Problem
 For
f(x) = -2x + 4
Evaluate
f(-3) = ?
Sample Problem
For
d(x) = -2x + 4
 Evaluate
d(4) =
?
Sample Problem
For
z(x) = -2x + 4
Evaluate z( e ) = ?
Conclusion
 You will have to practice more function
notation examples!
 This is an important topic that you should
develop a deep understanding of!
 So, let’s start practicing and understand the
function notation!