1.5 Library of Functions Classify functions and their graphs

Linear Functions (a line) Domain: All Realsy = mx + b Range : All RealsAx + By + C = 0 Y intercept (0, b)

Writing a linear function Let f(2) = 5; f(4) = 7Points (2, 5);(4, 7) Find the slope y – 5 = 1(x – 2)

Writing a linear function Let f(2) = 5; f(4) = 7Points (2, 5);(4, 7) Find the slope y – 5 = 1(x – 2) y – 5 = x - 2

Writing a linear function Let f(2) = 5; f(4) = 7Points (2, 5);(4, 7) Find the slope y – 5 = 1(x – 2) y – 5 = x – 2 y = x + 3f(x) = x + 3

Other linear function Constant functionf(x) = c f(X) = 4 (0,4)

Other linear function Identity functionf(x) = x (4, 4)

Squaring Function Domain: All Realsf(x) = ax 2 Range: Depends on the vertex (h, k) and a If a > 0 then Range greater then k If a < 0 then Range less then k Symmetry to the y axis (h, k) a> 0 a < 0 (h, k)

Cubic Function Domain: All Realsf(x) = x 3 Range : All Reals Symmetry to the origin

Square Root Function Domain: Range:

Reciprocal function Domain: x ≠ 0 Range : y ≠ 0 No intercepts Odd function Symmetry to The origin

Step Function (know as the Greatest integer function) The greatest integer less than or equal to x Rounding down to the last integer

Graph of the Step Function Domain: All Reals Range: { …, -2, -1, 0, 1, 2, 3 …}

How would the step graph change if ……. f (x) = [| x | ] + 3 f (x) = [| x + 2 | ] + 3 f (x) = - [| x |]

Is a Step function a Piecewise function?

Is a Step function a Piecewise function? YES Look at this Piecewise function and so on and so forth

Homework Page # 3, 15, 23, 29, 35, 39, 45, 53, 61, 70, 75

Homework Page # 11, 19, 27, 31, 37, 41, 49, 56, 67, 74