2.3) Functions, Rules, Tables and Graphs Purpose: To model functions using rules, tables, and graphs, and to identify symbolic expressions as functions Vocabulary: Function rule, function notation, independent variable, dependent variable

1) What is a function? A function is a relation between two variables such that each value of the first variable is paired with exactly one value of the second variable. The domain (x) of a function is the set of all possible values of the first variable. The range(y) of a function is the set of all possible values of the second variable.

2) When do you know that a function is in function notation 2) When do you know that a function is in function notation? when an equation is written in the form f(x)= instead of y =  y = 3x +2; f(x) = 3x + 2 3) Evaluate f(x) = -3x -10 for x = 5 4) Find the range of the given function for the domain {-2, 0, 5} ; f(x) = 2x + 1

5) How can you model a function 5) How can you model a function? By an equation, a table, a graph by mapping 6) What is the vertical-Line Test? A test that can help to determine if a graph represent a function. “If every vertical line intersects a given graph at no more than one point, then the graph represents a function.”

7) What are the values of the input and output 7) What are the values of the input and output? Input = independent variable = domain = x-value Output = dependent variable = range = y-value 8) What is a Relation? A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation

9) Identifying Functions Find the domain of each relation 9) Identifying Functions Find the domain of each relation. Determine whether each relation is a function. a) y = 3x -2 b) y = 1/3 + x c) x = y² 9) Make a table of values and graph each function then find the domain and range. a) f(x) = lxl -1 b) y = x²-1