Question

which relation is also a function?
a. {(-8,8), (-6,5), (-6,4), (-3,1), (-1,0)}
b. image of an ellipse on a coordinate plane
c. image of points on a coordinate plane

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value). In other words, no two ordered pairs in the relation can have the same x - value with different y - values. We can also use the vertical line test for graphs: if any vertical line drawn through the graph intersects the graph at more than one point, the graph does not represent a function.

Step2: Analyze Option A

For the set of ordered pairs \( \{(-8,8), (-6,5), (-6,4), (-3,1), (-1,0)\} \), we look at the x - values. The x - value \(-6\) appears twice, with corresponding y - values \(5\) and \(4\). Since one input (\(-6\)) has two different outputs (\(5\) and \(4\)), this relation is not a function.

Step3: Analyze Option B

The graph in Option B is an ellipse. If we apply the vertical line test, we can see that there are vertical lines that will intersect the ellipse at two points. For example, a vertical line drawn through the center of the ellipse (along the y - axis) will intersect the ellipse at two points (top and bottom). So, by the vertical line test, this graph does not represent a function.

Step4: Analyze Option C

For the graph in Option C, we apply the vertical line test. If we draw any vertical line, it will intersect the graph at most once. This means that each x - value (input) has exactly one y - value (output), so this relation is a function.

Answer:

C