Algebra II w/ trig

A. Greatest Integer function (Step Function): greatest integer less than or equal to x 1. =2. = 3. =4. = 5. =6. =

7., find f(6.9) 8., find f(-2.3)

9., find h(-2.3) 10., find h( 1 / 4 ) **Graph is a horizontal segment usually with one open endpoint.

B. Absolute Value Function: Part 1:  when a = 1, h = 0, k = 0 equation: this is the parents’ graphs for absolute value  when a = -1, h = 0, k = 0 equation: Vertex: (0, 0) when a is positive, it opens up when a is negative, it opens down

 when a = ½, h = 0, k = 0 equation:  when a = 3, h = 0, k = 0 equation:  vertex: (0, 0)  if a > 1, then _____  if a < 1, then _____

Part II:  when a = 1, h = 0, k = -2 equation:  when a = 1, h = 0, k = 2 equation: -if k is positive, _____ shifts ____ k units -if k is negative, ______ shifts ___ k units

Part III:  when a = 1, h = 3, k = 0 equation:  when a = 1, h = -3, k = 0 equation: -if h is negative, _____ shifts to the ____ h units -if h is positive, _____ shifts to the _____ h units

 Review  a: makes the graph narrower or wider and causes it to point up or down  k: shifts the graph up or down  h: shifts the graph right or left

Part IV. Without graphing predict which way the graph will shift from

Part V: Graph

C. Constant Function: or Graph of a linear function with a slope of 0 therefore it is a horizontal line 1. f(x) = 22. y = 3

D. Direct Function: or Has b = 0, passes through the origin, 1. y = 3x2. f(x) = -2x

E. Piecewise Function: consists of different function rules for different points of the domain You should be able to recognize what type of graph from the picture and from equations.

 2.7 Graphing Inequalities Linear inequality in two variables, x and y: where A and B cannot be equal to 0

 Graphing/Shading ≤ or ≥, use a solid boundary line, use a dashed boundary line **This line separates the coordinate plane into 2 half-planes*** **In one half-plane---all of the points are solutions of the inequality.** **In the other half-plane---no point is a solution.**

 Shade the appropriate region --- y < mx + b or y < mx + b, shade below boundary line when looking from left to right ---y ≥ mx + b or y > mx + b, shade above the boundary line when looking from left to right ---x ≤ c or x < c, shade to the left of the boundary line ---x ≥ c or x > c, shade to the right of the boundary line  Note: test by testing ONE point in the half plane. True, shade where the point is---False, shade on the opposite side

I. Graph A. x > yB. y < x + 2

C. -2x – 3y ≤ 3D. -5x – 2y > 4

E.F.