2.1 Relations and Functions

In this chapter, you will learn: What a function is. Review domain and range. Linear equations. Slope. Slope intercept form y = mx+b. Point-slope form y – y1 = m(x – x1). Linear regression.

What is a function? FUNCTION FUNCTION A function is a special type of relation in which each type of domain (x values) is paired of with exactly one range value (y value). NOT A FUNCTION NOT A FUNCTION FUNCTION NOT A FUNCTION FUNCTION

Relations and Functions Suppose we have the relation { (-3,1) , (0,2) , (2,4) } -3 2 1 2 4 FUNCTION ONE – TO – ONE DOMAIN x - values RANGE y - values

Relations and Functions Suppose we have the relation { (-1,5) , (1,3) , (4,5) } -1 1 4 5 3 FUNCTION NOT ONE – TO – ONE

Relations and Functions Suppose we have the relation { (5,6) , (-3,0) , (1,1) , (-3,6) } 5 -3 1 1 6 NOT A FUNCTION

Domain Range Domain and Range The set of all inputs, or x-values of a function. It is all the x – values that are allowed to be used. Range The set of all outputs, or y-values of a function. It is all the y – values that are represented.

Example 1 Domain = ________________ Range = _________________ All x – values or (-∞ , ∞) Domain = ________________ Range = _________________ Just 4 or {4}

Example 2 Domain = ________________ Range = _________________ Just -5 or {-5} All y – values or (-∞ , ∞)

Example 3 Domain = ________________ Range = _________________ All x – values or (-∞ , ∞) Domain = ________________ Range = _________________ From -6 on up or [-6 , ∞)

Example 4 Domain = ________________ Range = _________________ From -6 on up or [-6 , ∞) Domain = ________________ Range = _________________ All y – values or (-∞ , ∞)

Example 5 Domain = ________________ Range = _________________ All x – values or (-∞ , ∞) Domain = ________________ Range = _________________ All y – values or (-∞ , ∞)

Function Notation What is function notation? Function notation, f(x) , is called “f of x” or “a function of x”. It is not f times x . Example: if y = x+2 then we say f(x) = x+2. If y = 5 when x = 3, then we say f(3) = 5

Example 1 f(x) = 3x + 1 3 (5) + 1 = 16 f( 5) = ____________________ 3 (13) + 1 = 40 f( 13) = ____________________ 3 (-11) + 1 = -32 f( -11) = ____________________

Example 2 f(x) = x² + 3x - 5 5² + 3 (5) – 5 = 35 5² + 3 (5) – 5 = 35 f( 5) = ____________________ 0² + 3 (0) – 5 = -5 f( 0) = ____________________ 4² + 3 (4) – 5 = 23 f( 4) = ____________________