Question

does the relation shown below define a function?

yes
no

Explanation:

Step1: Recall the definition of a function

A relation is a function if every input (x - value) has exactly one output (y - value). In other words, for a graph, we can use the vertical line test: if any vertical line drawn through the graph intersects the graph at more than one point, then the relation is not a function.

Step2: Apply the vertical line test to the given graph

Looking at the graph (a parabola - like curve opening to the right), if we draw a vertical line (for example, a vertical line at \(x = 4\)), this vertical line will intersect the graph at two points (one in the upper part and one in the lower part of the curve). This means that for the input \(x = 4\), there are two different output \(y\) - values. So the graph fails the vertical line test.

Answer:

No