Question

graph the ordered pairs from the table. determine if the relation is a function.
(table with x and y values: x=-3,y=-4; x=0,y=5; x=1,y=-5; x=3,y=3)
(then four graph options with statements about whether the relation is a function: two say the relation is not a function, two say the relation is a function)

Explanation:

Step1: Recall the definition of a function

A relation is a function if for every input (x - value) there is exactly one output (y - value). In other words, no two ordered pairs have the same x - value with different y - values.

Step2: Analyze the given table

The table has the following ordered pairs: $(-3, - 4)$, $(0,5)$, $(1, - 5)$, $(3,3)$.

We check the x - values: - 3 appears once, 0 appears once, 1 appears once, and 3 appears once. There are no repeated x - values with different y - values.

Step3: Analyze the graphing (conceptually)

When we graph these ordered pairs, each x - coordinate will have only one corresponding y - coordinate. So, by the definition of a function, this relation is a function.

Answer:

The relation is a function (and the correct graph should plot the points $(-3, - 4)$, $(0,5)$, $(1, - 5)$, $(3,3)$ and the option that states "The relation is a function" is correct).