The document discusses functional notation and evaluating functions. Some key points: - Functional notation f(x) represents a variable y in an equation, like writing f(x)=2x+6 for the equation y=2x+6. - To evaluate a function, substitute the given value for x into the function. For example, if f(x)=2x+6 then f(3)=2(3)+6=12. - Examples are given of evaluating various functions for different values of x.

1. Ade John T. Gestole, T1

2. 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.

3. 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

4. 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

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

6. Exercise:

7. Determine the value of x
when given f(x).
•Given f(x) = 4x + 8, determine x
when:
f(x) = 2
f (x) = -1

8. Exercise:

9. Evaluating More Functions
If f(x) = 3x  1, and g(x) = 5x + 3, find each:
= [3(2) -1] + [5(3) + 3]
= 6 - 1 + 15 + 3
= 23
= [3(4) - 1] - [5(-2) + 3]
= 11 - (-7)
= 18
= 3[3(1) - 1] + 2[5(2) + 3]
= 6 + 26
= 32
1. f(2) + g(3)
2. f(4) - g(-2)
3. 3f(1) + 2g(2)