Functions And Function Notation

Definitions Relation A relationship between sets of information. Typically between inputs and outputs. Function A relation such that there is no more than one output for each input. (each x should have a single unique y) (Must pass the vertical line test)

4 Examples of Functions X Y 10 2 15 -5 18 20 1 7 X Y -3 1 -1 4 5 7 3

3 Examples of Non-Functions Y 4 1 10 2 11 -3 5 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.

Functional Notation Cont’d Example: y = 2x + 6 can be written as f(x) = 2x + 6. Another example: z = 3g + 1 can be written as f(g) = 3g+1. Write the following in function notation: 1. w = -2r w(r) = -2r or f(r) = -2r 2. p = 5v – 4 p(v) = 5v – 4 or g(v) = 5v – 4

Functional Notation Con’t Given the equation y = 2x + 6, evaluate when x = 3. y = 2(3) + 6 y = 12 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

Evaluating Functions Given f(x) = 4x + 8, find each: f(2) 2. f(a +1) = 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

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