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Warm up Find the domain and range of the following relation: x -2 0 5 6 y -3 -1 0 3 4 D: R:

Relation Notation Example: A relation R is denoted by x 4 x – 3 “x is mapping to 4 x – 3” OR R = {(x, y): y = 4 x – 3} Find the range of R for the domain {0, 1, 2, 3} **We find the range by substituting each x-value individually into the relation and simplifying

Example: A relation R is denoted by x -2 x 2 – 1 x is mapping to -2 x 2 – 1 1. Find the range of the relation R for the domain {1, 2, 3, 4} 2. Find the range of the relation R for the domain {-4, -3, -2, -1}

Graphing a relation X -3 -2 -1 0 1 2 3 y Draw the graph of the relation R= {(x, y): y=2 x} Start with a table Ordered pairs:

Warm Up Represent the relation R={(-3, 5), (0, 4), (0, 2), (3, 4)} In a mapping diagram and a graph

Finding Domain and Range from a Graph • Example: Our previous graph of y=2 x. Let’s find the domain and range! • Since the domain is the x-values or inputs, we look at the horizontal span of the graph • Since the range is the y-values or outputs, we look at the vertical span of the graph

Find the domain and range Domain: Range:

Finding Domain and Range from an equation • When finding the domain, look for what can’t happen: – Zero in the denominator or – Negatives under a square root. • When finding the range, it is easiest to look at the graph to see what y-values are possible for the graph – Or you can solve the equation for x and see what values are possible for y • Example: Our previous equation y=2 x. Let’s find the domain and range!