Complete W.A.M 9-12

SLM I can describe the characteristics of a function. I can recognize a function in any form. I can determine if relations are functions. I can tell how a function is different from a relation I can tell why it is important to know which variable is the independent variable. I can determine the best way to represent a function. I can represent relations and functions using tables, graphs, words, and algebraic equations.

Now try to fill out the other side using these ordered pairs: (3, 8), (-4, 5), (2, 3), and (3, 1)

Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}

Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 1 3 -6 4

Functions A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.

Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.

Y = 3x +1 Y = 2x Equations of a Function Some functions can be written as equations in two variables. The independent variable represents the input (x) of a function. The dependent variable represents the ouput(y) of a function. y = x2 -3 y = x3 Y = 3x +1 *always make a table of values to make sure your independent variable (x) does not repeat Y = 2x

Graphs of a Function Vertical Line Test: If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function.

Does the graph represent a function? Name the domain and range. x y Yes Bc the x value does not repeat x y

Does the graph represent a function? Name the domain and range. x y No Bc the x value does repeat/ ex: (3,2) and (3,- 1) Bc the x value does repeat/ ex: (2,4) and (2, - 5) x y

Does the graph represent a function? Name the domain and range. x y Yes Bc the x value does not repeat No Bc the x value does repeat. Ex. (2,0), (2,1). Etc… x y

Lesson 1 function Handout: Independent 1. Is the (name, shirt color) a function? Why or Why not? 2. Prove your reasoning by mapping 3. Is the (shirt color, name) a function? Why or Why not? 4. Prove your reasoning by mapping

5. Is the (name, shirt color) a function. Why or Why not. 6 5. Is the (name, shirt color) a function? Why or Why not? 6. Prove your reasoning by mapping 7. Is the (shirt color, name) a function? Why or Why not? 8. Prove your reasoning by mapping

TOD: What are characteristics of a function?