Question

create your own examples and non - examples of functions for each representation below.
examples
non - examples
{((_,_)(_,_)(_,_)}
{((_,_)(_,_)(_,_)}
table with x and y columns for examples
table with x and y columns for non - examples
coordinate grid for examples
coordinate grid for non - examples

Explanation:

Step1: Define function criteria

A function is a relation where each input ($x$-value) has exactly one output ($y$-value).

Step2: Create function examples

• Ordered Pairs: Assign unique $x$-values to unique $y$-values: $\{(0, 1), (1, 2), (2, 3)\}$
• Table: Use linear rule $y=2x$, assign unique $x$s to $y$s as shown.
• Graph: Plot points where no vertical line intersects more than once.

Step3: Create non-function examples

• Ordered Pairs: Repeat an $x$-value with different $y$s: $\{(0, 1), (0, 2), (1, 3)\}$
• Table: Repeat an $x$-value with different $y$s as shown.
• Graph: Draw a vertical line, which fails the vertical line test.

Answer:

EXAMPLES:

1. Ordered Pairs: $\{(0, 1), (1, 2), (2, 3)\}$
2. Table:

x	0	1	2	3	4

1. Graph: A straight line passing through points $(0,0)$, $(1,1)$, $(2,2)$ (linear graph passing vertical line test)

NON-EXAMPLES:

1. Ordered Pairs: $\{(0, 1), (0, 2), (1, 3)\}$
2. Table:

x	0	0	1	2	3

1. Graph: A vertical line at $x=1$ (fails vertical line test)