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.

Analyzing the first graph:

For any vertical line (fixed \( x \)-value), we check how many times it intersects the graph. The first graph (left) is a piecewise linear graph. For every \( x \)-value, a vertical line will intersect the graph at most once. Thus, it passes the vertical line test and is a function.

Analyzing the second graph:

The second graph (right) is a horizontal line (or a line with very small slope). For any vertical line (fixed \( x \)-value), it intersects the graph exactly once. Thus, it also passes the vertical line test and is a function.

Answer:

Both the first (left) and second (right) graphs represent functions.