1.6 A Library of Parent Functions I. Step and Piecewise-Defined Functions. A) Functions whose graphs resemble stair-steps are know as Step Functions. B) Greatest Integer Function: a step function. 1) Symbol f(x) = 2) It means the greatest integer (whole #) less than or equal to x. 3) Examples:

1.6 A Library of Parent Functions II. Parent Functions and their Graphs. A) Straight Line(s) Graphs: 1) y = mx + b or f(x) = mx + b (where b = the y-intercept, m = the slope) 2) Vertical lines: x = # 3) Horizontal lines: y = # or f(x) = # 4) Absolute value: y = or f(x) = a) It is V shaped. b) For the vertex is at (–B,C)

1.6 A Library of Parent Functions II. Parent Functions and their Graphs. B) Curved Graphs: 1) Square root: y = 2) Cubed root: y = 3) Quadratic: y = x2 4) Cubic: y = x3

1.6 A Library of Parent Functions II. Parent Functions and their Graphs. C) Special Graphs: 1) Reciprocal: y = 2) Greatest Integer: y = 3) Piece-wise: f(x) = HW: page 71 # 37–49 odd, 53–60 all