Domain and Range

Domain: The domain is all the values that x is allowed to take on.

RANGE:

Domain and Range Notation Set Notation Set Builder Notation Inequality Notation Interval Notation You may use any type of notation, unless the problem requires a particular type. If one type is used somewhere in the problem, however, use that type of notation for consistency.

Examples for Discrete Data: Set Notation x{-2,0,1,6} “x is an element of the set -2, 0, 1, and 6” Set Builder Notation {x|x=-2,0,1,6} “The set of all Xs such that x = -2, 0, 1, or 6” Examples for Continuous Data Set Builder Notation {x|-7<x<5} Inequality Notation -7<x<5 Interval Notation (-7,5)

Set Builder and Inequality Set Builder Notation Inequality Notation “The set of all Xs, such that x is greater than or equal to -3 and less than 5” “x is greater than or equal to -3 and less than 5” Set Builder Notation and Inequality Notation are almost the same. You can use either one.

Interval Notation for Domain and Range “X is greater than or equal to -3 and less than 5.” Range [ greater than or equal to ] less than or equal to ( greater than ) less than “Y is greater than zero and less than or equal to 7.”

You can find domain & range given a variety of modes: Table Set of points Mapping Equation Graph Situation

Table Domain: x{2,3,4} Range: y {3,5,7,9} NO Function? _____ x y 4 3 Why, because for x=4 there are two different values for y. For every input there can only be one output

Set of Points Domain: {x|x=-3,-1,1,2} Range: {y|y=0,1,2,3} {(1,0), (-1,1), (2,2), (-3,3)} Domain: {x|x=-3,-1,1,2} Range: {y|y=0,1,2,3} Function? _____ Yes Why, because for input, x there is only one output for y

Mapping 7 2 9 3 4 6 -1 Function? _____ x y Domain: {x|x=-1,2,4,7} Range: {y|y=3,6,9} YES Function? _____ Why, because for every x input there is only one y output.

Range: {y|y=-1,74} Equation Find the range of the given equation when the domain is {x| x= -5, 0, 5}: Range: {y|y=-1,74} How, substitute each of the x values in the equation and work it out: OR, put the equation in your calculator and go to table and find the y values

y = 5x - 1 Domain: x < 3 Range: y<14 Equation How, substitute x=3 in the equation: y=5(3)-1=14 OR, put y=5x-1 in your calculator, go to 2nd Table and see what the y values are.

Situation Maria earns $7 per hour for baby-sitting after school and on Saturday. She works no more than 16 hours a week. Independent: Time Dependent: Amount of Money Domain: Range:

Graph D:x{-3,-2,0,2} R:y{-1,0,3,4} (0, 4) (-2, 3) This is a DISCRETE Graph since the points are not connected (-3, 0) (2, -1)

Graph D: R: 4 This graph is a CONTINUOUS graph since the points are connected. - 6 5 - 4

LET’S PRACTICE!