The document explains functional notation, illustrating how equations expressed as functions can be transformed. It provides examples of evaluating functions for specific values and finding outputs based on given inputs. Additionally, it presents methods for determining variable values when given function outputs.

3. Functional Notation
An equation that is a function may
be expressed using functional
notation.
The notation f(x) (read “f of (x)”)
represents the variable y.

4. Example:
y = 2x + 6 can be written as f(x) = 2x + 6.
Given the equation y = 2x + 6, evaluate when x = 3.
y = 2(3) + 6
y = 12
Functional Notation Cont’d

5. For the function f(x) = 2x + 6, the notation f(3)
means that the variable x is replaced with the
value of 3.
f(x) = 2x + 6
f(3) = 2(3) + 6
f(3) = 12
Functional Notation Con’t

6. Given f(x) = 4x + 8, find each:
1. f(2)
2. f(a +1)
3. f(4a)
Evaluating Functions
= 4(2) + 8
= 16
= 4(a + 1) + 8
= 4a + 4 + 8
= 4a + 12
= 4(-4a) + 8
= -16a+ 8

7. For the function f(x) = -5x + 11, determine:
a) f(1)
b) f(-3)
c) f(0)
= -5(1) + 11
= -5 + 11
= 6
= -5(-3) + 11
= 15 + 11
= 21
= -5(0) + 11
= 0 + 11
= 11

8. Determine the value of x when given f(x).
Given f(x) = 2(4x + 8), determine x
when:
f(x) = 2 f(2)
f (x) = -1 f(-1)
= 2{4(2) + 8}
= 2(8 + 8)
= 2(16)
= 32
= 2{4(-1) + 8}
= 2(-4 + 8)
= 2(4)
= 8