Question

does the relation shown below define a function? no yes

Explanation:

Step1: Recall the definition of a function

A relation is a function if for every input \( x \)-value, there is exactly one output \( y \)-value. One way to test this is the vertical line test: if any vertical line drawn through the graph intersects the graph at more than one point, the relation is not a function. If every vertical line intersects the graph at most once, then it is a function.

Step2: Apply the vertical line test to the given graph

Looking at the graph (a parabola opening downward), if we draw any vertical line (a line parallel to the \( y \)-axis) through the graph, it will intersect the graph at most once. This is because for each \( x \)-value, there is only one corresponding \( y \)-value on the parabola.

Answer:

Yes