Writing a Function Rule Write a function rule for situation C is 8 more than half of n. 2.5 more than the quotient of h and 3 is w. y is 2 less than the product of 7 and x.

More Writing a Function Rule Write a function rule for situation The total distance d traveled after n hours at a constant speed of 45 miles per hour. A worker’s earnings e for n hours when the worker’s hourly wage is $6.37. The volume V of a cube when you know the length n of a side. Suppose a plumber gets paid $60 for traveling time to a job plus $115 for each hour he takes to complete the job. The plumber charges for whole-number hours.

Even More Writing Function Rules Suppose you borrow money from a relative to buy a lawn mower for $245. You charge $18 to mow a lawn. Write a rule to describe your profit P as a function of the number of lawns mowed n. If you mow 3 lawns a day Monday through Friday, how much profit will you make? At a supermarket salad bar, the price of a salad depends on its weight. The salad costs $.05 for the container plus $.18 per ounce. a) Write a rule to describe the function. b) How much would a 9 ounce salad cost?

Definition of a Function A function is a set of ordered pairs in which no two ordered pairs of the form (x, y) have the same x-value with different y-values. That sounds easy enough. Maybe we should look at some examples. Example 1 This is a function because there are no repeating x-values. (-3, 9) (-2, 4) (-1, 1) (0, 0) (1, 1) (2, 2) (3, 3) Example 2 This is not a function because there are repeating x-values. (5, 7) (3, 5) (1, 4) (0, 0) (1, 6) (4, 2) (6, 3) Example 2 is a relation. That was easy

Mapping Diagrams That was easy Make mapping diagrams for each of the following relations. Then determine if the relation is a function. (0, 2) (1, 3) (2, 4) (-1, -2) (3, 6) (-5, -10) (3, 2) (-2, 8) (-1, 5) (0, 8) (-1, 3) (2, 3) (0, 2) (1, 4) (2, 6) (3, 4) (4, 2) 1 2 2 3 4 -5 -1 3 -10 -2 2 6 1 2 3 4 2 4 6 -2 -1 2 3 5 8 Is a Function Not a Function Not a Function Is a Function That was easy

Vertical Line Test A graph represents a function if any vertical line drawn intersects it in at most one point. The vertical line never intersects the graph in more than one point, therefore this is a function. The vertical line never intersects the graph in more than one point, therefore this is a function. The vertical line does intersect the graph in more than one point, therefore this is not a function.

Applying the Vertical Line Test Use the vertical line test to determine whether each relation is a function. Asi De Facil (-4, -2) (-2, 1) (-1, 4) (2, 1) (4, -3) (-4, -4) (-4, 2) (0, 1) (2, 4) (4, -4) (-3, 1) (-1, -3) (-1, -1) (-1, 1) (2, 2) (2, 4) 4 2 -2 -4 4 2 -2 -4 4 2 -2 -4 -4 -2 2 4 -4 -2 2 4 -4 -2 2 4 The vertical line never intersects the graph in more than one point, therefore this is a function. The vertical line does intersect the graph in more than one point, therefore this is not a function. The vertical line does intersect the graph in more than one point, therefore this is not a function.

Do Not Identify Domain & Range Homework Page 265: 8 – 20 Even Numbers Volume of a Cylinder = Page 271: 8 -15 All Questions Do Not Identify Domain & Range

Function Notation x = y = f(x) = For any function f, the notation f(x) is read “ f of x” and represents the value of y when x is replaced by the number or expression inside the parenthesis. Input Value Independent Variable x = Domain y = f(x) = Output Value Dependent Variable Range Domain Set of all independent variables for which a function is defined. All x-values. Range Set of all dependent variables for which a function is defined. All values of f(x).

Making a Table for a Function Make a table for the function using the following domain. {0, 1, 2, 3, 4} x -3 1 2 3 4 -1 1 3 5 That was easy

Finding Domain and Range Write the ordered pairs for the relation shown in the graph and find the domain and range for each example. 4 2 -2 -4 4 2 -2 -4 4 2 -2 -4 -4 -2 2 4 -4 -2 2 4 -4 -2 2 4 (-4, -2) (-2, 1) (-1, 4) (2, 1) (4, -3) (-4, -4) (-4, 2) (0, 1) (2, 4) (4, -4) (-3, 1) (-1, -3) (-1, -1) (-1, 1) (2, 2) (2, 4) Domain {-4, -2, -1, 2, 4} Domain {-4, 0, 2, 4} Domain {-3, -1, 2} Range {-3, -1, 1, 2, 4} Range {-3, -2, 1, 4} Range {-4, 1, 2, 4, } Asi De Facil

Finding the Range for a Given Domain Find the range of each function for the domain x f(x) x f(x) x f(x) -2 0.7 2.3 -7 -2 0.7 2.3 8 -2 0.7 2.3 3 -1.6 -0.1 -4.02 1.6 -4.9 5.58 Range {-7, -1.6, 1.6} Range {8, -0.1, -4.9} Range {3, -4.02, 5.58} That was easy Asi de facil

Using a Table to Represent Functions Determine if each relation is a function and if so state the domain and the range. x y x f(x) x f(x) 1 2 3 4 3 5 7 9 -3 5 6 2 4 -1 2 7 11 14 2 7 11 14 Yes Domain {1, 2, 3, 4} No Yes Domain {2, 7, 11, 14} Range {3, 5, 7, 9} Range {2, 7, 11, 14} x f(x) x y x y 2 5 -1 -4 -8 -7 -2 -1 1 3 5 -6 4 -1 -2 1 2 3 4 No Yes Domain {-2, -1, 0, 1} No Range {3, 5, -6, 4}

Identify Domain & Range Only Homework Page 271: 8 – 11 Identify Domain & Range Only Page 272: 18, 20, 24, 25