Question

1. which of these could represent a function? select all that apply

a. ( y = \frac{2}{3}x - 5 )
( square ) b. ( x = 4 )
( square ) c.
image of an ellipse on a coordinate plane
( square ) d.

( x )	( y )
-3	7
-2	7
-1	7

Explanation:

Step1: Recall function definition

A relation is a function if each input ($x$-value) has exactly one output ($y$-value). We use the vertical line test for graphs, and check $x$-value uniqueness for equations/tables.

Step2: Analyze Option A

Equation: $y = \frac{2}{3}x - 5$
This is a linear equation. For every $x$, there is exactly one $y$. So it is a function.

Step3: Analyze Option B

Equation: $x = 4$
This is a vertical line. For $x=4$, there are infinitely many $y$-values. It fails the vertical line test, so it is not a function.

Step4: Analyze Option C

Graph: Horizontal ellipse
A vertical line will intersect the ellipse at two points. It fails the vertical line test, so it is not a function.

Step5: Analyze Option D

Table: All $x$-values map to $y=7$
Each $x$-value has exactly one $y$-value (even if multiple $x$s share the same $y$). So it is a function.

Answer:

A. $y = \frac{2}{3}x - 5$, D. (the table where all $x$-values correspond to $y=7$)