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? 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). FUNCTION NOT A FUNCTION FUNCTION NOT A FUNCTION

Relations and Functions Suppose we have the relation { (-3,1), (0,2), (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) } FUNCTION NOT ONE – TO – ONE

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

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. 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 (- ∞, ∞) Just 4 or {4}

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

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

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

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

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 What is function notation?

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

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