Question

select a cell in each row to indicate if the item is a function or not a function.

	function	not a function
$(2, 3), (2, 4), (2, 5), (2, 6)$	3	✔️
$(1, 2), (2, 2), (3, 2), (4, 2)$	✔️	6
$(1, 2), (2, 3), (3, 4), (4, 5)$	✔️	8
$x = -3$	✔️	10

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (y - value). For equations, vertical line test: a vertical line \(x = a\) intersects a function at most once; horizontal line test is for one - to - one, not just function. For ordered pairs, check if any x - value is repeated with different y - values.

Step2: Analyze \(y = 0\)

The equation \(y = 0\) is a horizontal line. For any x - value, the y - value is 0. So each x has exactly one y (0). So it is a function. So we should select "Function" (the cell with 1).

Step3: Analyze \((2,3),(2,4),(2,5),(2,6)\)

Here, the x - value 2 is paired with multiple y - values (3, 4, 5, 6). So it fails the function definition (one x has multiple y's). So it is not a function (already selected correctly as "Not a Function" with 2).

Step4: Analyze \((1,2),(2,2),(3,2),(4,2)\)

Each x - value (1, 2, 3, 4) has exactly one y - value (2). So it is a function (selected correctly as "Function").

Step5: Analyze \((1,2),(2,3),(3,4),(4,5)\)

Each x - value (1, 2, 3, 4) has exactly one y - value (2, 3, 4, 5 respectively). So it is a function (selected correctly as "Function").

Step6: Analyze \(x=-3\)

The equation \(x = - 3\) is a vertical line. A vertical line will have infinitely many y - values for the same x - value (-3). So it fails the vertical line test (one x has multiple y's). So it is not a function. So we should select "Not a Function" (the cell with 10).

Answer:

• For \(y = 0\): Select "Function" (the cell with 1).
• For \((2,3),(2,4),(2,5),(2,6)\): Correctly selected "Not a Function" (the cell with 2).
• For \((1,2),(2,2),(3,2),(4,2)\): Correctly selected "Function".
• For \((1,2),(2,3),(3,4),(4,5)\): Correctly selected "Function".
• For \(x=-3\): Select "Not a Function" (the cell with 10).