1. 2.1: Relations and Functions
Perfection is a road, not a destination. Every time you live, you get an education.

2. Relation Ex1) Graph the coordinate points: (–3, 3), (2, 2), (–2, –2),
(0, 4), (1, –2)
A relation is a set of pairs of input (x) and output (y) values.
Written:
{(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.

3. Relation {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}
Domain – the set of all inputs of a function (x-coordinates)
Domain: {-3, -2, 0, 1, 2 }
Range - the set of all outputs of a function (y-coordinates)
Range: { -2, 2, 3, 4 }

4. Relation Ex2) Write the ordered pairs for the relation.
Find the domain and range.

5. Mapping Diagrams Ex3) {(–3, 3), (2, 2), (–2, –2), (0, 4), (1, –2)}.
Domain
Range

6. Functions
A function is a relation in which each input value is paired with only one output value.
Domain
Range
Domain
Range 2 3 4 7 5 6 8 -2 5 -1 3 4
Function?
Function?

7. Vertical Line Test
Vertical Line Test: If a vertical line passes through at least two points on the graph, the relation is not a function.
Ex4) {(-2, -1), (0, 3), (-2, 3), (5, 4)}
Ex5) {(3, 6), (2, 6), (7, 8), (4, 5)}

8. Vertical Line Test
Ex6) Are these relations functions?

9. Function Notation

10. Function Notation
Ex8) The surface area of a cube is a function of the length of a side of the cube. Write a function for the surface area of the cube. Find the surface area of the cube with a side 2 inches long.

11. 2.1: Relations and Functions
HW: 7, 12, 13, 17, 20, 21, 23, 25, 33, 37, 39, 41, 46, 47
Perfection is a road, not a destination. Every time you live, you get an education.