Question

which of these relations are functions? select all that apply.

Explanation:

To determine if a relation is a function, we use the vertical line test: a graph represents a function if no vertical line intersects the graph more than once.

Step 1: Analyze the first graph (top - left)

This graph has a curve that loops, so a vertical line would intersect it more than once. Thus, it is not a function.

Step 2: Analyze the second graph (top - right)

This graph also has a curve that loops, so a vertical line would intersect it more than once. Thus, it is not a function.

Step 3: Analyze the third graph (bottom - left, a circle)

A circle is symmetric, and a vertical line will intersect the circle at two points (except at the top and bottommost points). So, it fails the vertical line test and is not a function.

Step 4: Analyze the fourth graph (bottom - right, a piece - wise linear graph)

For this graph, any vertical line will intersect the graph at most once. So, it passes the vertical line test and is a function.

Answer:

The relation represented by the bottom - right graph (the piece - wise linear graph) is a function.