Question

1. identify all relations that represent functions. (place a checkmark in the box for all that apply)

x	1	2	3	4
y	-1	0	5	-1

(arrow diagram with x: 2,5,7,9 and y: 0,3,4,8)

{(-4, 2), (-1, -7), (0, 5), (5, 2)}

(graph with two lines meeting at origin)

(graph of a parabola opening downward)

(arrow diagram with x: -4,-1,0,5 and y: -7,-2,3)

Explanation:

Step1: Recall Function Definition

A relation is a function if each input (x - value) has exactly one output (y - value). We'll check each relation:

Step2: Check First Table (Top - Left)

The table has x - values 1, 2, 3, 4. Each x has one y (1→ - 1, 2→0, 3→5, 4→ - 1). Repeating y - values are okay, as long as each x has one y. So this is a function.

Step3: Check First Mapping Diagram (Top - Middle)

x - value 5 maps to 3, 4, and 8 (multiple outputs for x = 5). So this is not a function.

Step4: Check Ordered Pairs (Top - Right)

The ordered pairs are (- 4, 2), (- 1, - 7), (0, 5), (5, 2). Each x (- 4, - 1, 0, 5) has one y. So this is a function.

Step5: Check First Graph (Bottom - Left)

This graph has a vertical line (or a "V" - shape with a common vertex) where an x - value (at the vertex) would have multiple y - values (since two lines meet at the vertex, same x, different y). So this is not a function (fails vertical line test).

Step6: Check Second Graph (Bottom - Middle)

This is a parabola opening downward. The vertical line test: any vertical line will intersect the graph at most once. So this is a function.

Step7: Check Second Mapping Diagram (Bottom - Right)

x - value 0 maps to - 2 and 3 (multiple outputs for x = 0), and x - value 5 maps to - 2 and 3. So this is not a function.

Answer:

The relations that are functions are:

• The top - left table (with x: 1, 2, 3, 4 and y: - 1, 0, 5, - 1)
• The top - right set of ordered pairs {(- 4, 2), (- 1, - 7), (0, 5), (5, 2)}
• The bottom - middle parabola graph