1. FUNction Notation

2. Function Notation This relation is a FUNCTION.f = { (1, 7), (2, 14), (3, 21), (4, 28) } The equation for this relation is y = 7x. x is the independent variable y is the dependent variable We say the value of y depends on the value of x in the equation above. We say y is a function of x which is written as y = f (x) In this case, parentheses DO NOT indicate multiplication. Do not read f(x) as f times x. Find f(5) and f(6). y = 7x  f(x) = 7x f(5) = 7 · 5 Read f(x) as “f of x.” For example, when x = 2, y = 14, it can be written as f(2) = 14 which is read as “f of 2 is 14.” f(5) = 35 f(6) = 7 · 6 f(6) = 42

3. The FUNction Machine http://207.207.4.198/pub/flash/9/9.html

4. Functional relationships can be represented in a variety of ways. MethodDescriptionExample Written Description Ordered pairs Mapping Table 12341234 7 14 21 28 x1234 y7142128 MethodDescriptionExample Equation Function Notation Graph Use words to describe the functional relationship. y equals 7 times a number, x. List the ordered pairs. { (1,7), (2,14), (3,21), (4,28) } Draw a picture that shows how the ordered pairs are formed. Place the ordered pairs in a table. Write a equation that describes the y-coordinate in terms of the x-coordinate. y = 7x x = ind. var. y = dep. var. Write a special type of equation that uses f(x) to represent y. f(x) = 7x Graph the ordered pairs.

5. Practice using function notation. Given f(x) = 5x – 11, find f(-8) and f(0). Given g(x) = 2x 2 + 3, find f(-3) and f(5). Given the domain is { 1, 2, 3, 4} and p(x) = 4 – 6x, find the range. Given the domain is { -3, 0, 2, 7} and t(x) = –x + 1, find the range. Given h(x) =, find h(-2) and h(7).

6. More practice!!!