Question

the image contains four coordinate plane graphs (with x-y axes, grids) showing different curves/lines: 1) a piecewise graph and a line; 2) a left-opening curve and a downward curve; 3) two lines through the origin; 4) a hyperbola-like curve. each graph has a selection circle below.

Explanation:

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

Analyzing Each Graph:

1. First Graph (Top-Left):

A vertical line (e.g., \( x = 1 \)) would intersect the graph at two points (the "corner" and the line). Fails the vertical line test. Not a function.

1. Second Graph (Top-Middle):

A vertical line (e.g., \( x = -1 \)) intersects the graph at two points (the upper and lower curves). Fails the vertical line test. Not a function.

1. Third Graph (Top-Right):

Any vertical line intersects the graph at only one point. Passes the vertical line test. This is a function.

1. Fourth Graph (Bottom-Right):

Any vertical line intersects the graph at only one point. Passes the vertical line test. This is also a function, but the top-right graph is a linear function (straight line), while the bottom-right is a curve (likely a hyperbola or similar). Assuming the question asks for the linear function (or the most straightforward function), the top-right graph is the clearest choice.

Answer:

The graph in the top-right (third graph) represents a function.