Lesson 5.2 (PART 2). Functional Notation An equation that is a function may be expressed using...

Lesson 5.2 (PART 2)

Functional NotationAn equation that is a function may be expressed using functional notation.

The notation f(x) (read “f of (x)”) represents the variable y.

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

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) + 6f(3) = 12

Functional Notation Con’t

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

Determine the value of x when given f(x).

Given f(x) = 4x + 8, determine x when:

f(x) = 2

f (x) = -1

If f(x) = 3x 1, and g(x) = 5x + 3, find each:

Evaluating More Functions

= [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)