Question

1. the set of ordered pairs shown is missing an x - value. {(9, - 15), (0, 0), (4, 0), (___, 2)}

a. give an example of an x - value that would result in y as a function of x.
b. give an example of an x - value that would not result in y as a function of x.
create your own examples and non - examples of functions for each representation below.

examples	non - examples
(table with x and y columns)	(table with x and y columns)
(coordinate grid)	(coordinate grid)

Explanation:

Part 10a and 10b (Function Definition: A relation is a function if each input \( x \) has exactly one output \( y \))

10a: Example of \( x \)-value for function

Step1: Recall function definition

A function requires each \( x \) to map to one \( y \). The existing \( x \)-values are \( 9, 0, 4 \). We need an \( x \) not in \( \{9, 0, 4\} \).

Step2: Choose a new \( x \)-value

Let’s pick \( x = 5 \). Now the ordered pairs are \( \{(9, -15), (0, 0), (4, 0), (5, 2)\} \). Each \( x \) (9, 0, 4, 5) has one \( y \), so this is a function.

Answer:

(10a): \( 5 \) (any \( x \) not in \( \{9, 0, 4\} \) works, e.g., \( 1, 2, -1 \), etc.)

10b: Example of \( x \)-value for non - function

Step1: Recall non - function condition

A relation is not a function if an \( x \) has more than one \( y \). So we use an existing \( x \)-value (9, 0, or 4), since those already have a \( y \)-value.

Step2: Choose an existing \( x \)-value

Let’s pick \( x = 9 \). Now the ordered pairs would be \( \{(9, -15), (0, 0), (4, 0), (9, 2)\} \). Here, \( x = 9 \) maps to \( -15 \) and \( 2 \), so it’s not a function.