Evaluating Functions

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