Algebra 1 Unit 1 Section 1 6 Notes

Algebra 1 Unit 1 Section 1. 6 Notes: Relations

Coordinate System: The grid formed by the intersection of two number lines, the horizontal axis and the vertical axis.

Ordered pair: location of any point on a coordinate plane, written in the form (x, y). x-coordinate: the first number in an ordered pair. y-coordinate: the second number in an ordered pair.

Relation: a set of ordered pairs Domain: the set of first numbers ofthe ordered pairs in a relation. Range: the set of second numbers of the ordered pairs in a relation. Mapping: illustrates how each element of the domain is paired with an element in the range.

In the relation above, the domain is {-2, 0, 1} and the range is {-3, 2, 4}

Example 1 a) Express {(4, 3), (-2, -1), (2, -4), (0, -4)} as a table, a graph, and a mapping. b) Determine the domain and range of the relation.

Independent variable: the variable in a relation with a value that is subject to choice. Dependent variable: the variable in a relation with a value that depends on the value of the independent variable. *If you change the independent variable, then the dependent variable changes too!

Example 3 Identify the independent and the dependent variable for each relation. a) In warm climates, the average amount of electricity used rises as the daily average temperature increases and falls as the daily average temperature decreases. b) The number of calories you burn increases as the number of minutes that you walk increases.

Example 3 A relation can be graphed without a scale on either axis. These graphs can be interpreted by analyzing their shape. Describe what is happening in each graph. a) b)