SECTION 1.2 Functions

Relations A relation is a set of ordered pairs.  Set of x-values is the DOMAIN  Set of y-values is the RANGE If each x-value corresponds with exactly one y-value, then the relation is a FUNCTION List the elements in the domain and range for the following relation. Is the relation a function? {(2, 1) (3, 5) (-1, 4) (5, 9)}  Domain: {-1, 2, 3, 5}  Range:{1, 4, 5, 9}  Yes, it is a function.

Your turn… Name the domain and range for the relation. Is it a function? {(-1, 8) (-2, 3) (5, 7) (-2, 5) (3, 9)} Domain:{-2, -1, 3, 5} Range:{3, 5, 7, 8, 9} No, it is not a function. (-2 repeats…)

Function Notation For equations that are functions, we can use function notation: f(x) We can use the notation f(3) instead of “find the value of y when x = 3” Remember that you need to replace all x’s in the function with the x-value in order to evaluate. f(x) = 2x 2 – 3x + 4, find f(1) f(1) = 2(1) 2 – 3(1) + 4 f(1) = 2 – f(1) = 3

Your turn: f(x) = 3x 2 + 5x – 10 f(2) 12 f(-3) 2 f(a + 1) 3(a + 1) 2 +5(a+ 1) – 10 or 3a a -2

Assignment Pages 90 – 91 Problems 2 – 30 evens

Vertical Line Test

Domains of Functions Most functions have a domain of All Real Numbers. In other words, you can use any number for x and get a real y-value. Functions that don’t have All Real Numbers for their domain are:  Radical functions  Rational functions Let’s see how to find domains of these functions.

Finding Domains For radical functions: Since you can’t √ a (-) number:  Set what’s under the radical > 0 and solve for x.  After you solve, you have the domain For rational functions: Since you can’t divide by zero:  Set denominator = o and solve for x.  After you solve, the domain is everything except x.

Sample Problems… Find the domain: f(x) = 7x + 3  Domain = All Real Numbers f(x) = √8 – x  8 – x > 0  8 > x; Domain is all numbers x < 8 f(x) = x – x  2 – x = 0  2 = x; Domain is all numbers except 2

Your turn: Find the domain: f(x) = √7 – x Domain is all numbers x < 7 f(x) = 10 x + 3 Domain is all real numbers except -3

Assignment Pages 94 – 95 Problems 52 – 72 evens