Question

which graphs represent functions? select all that apply.

Explanation:

Step1: Recall Vertical Line Test

A graph represents a function if no vertical line intersects the graph more than once.

Step2: Analyze Top - Left Graph

For the top - left graph, if we draw a vertical line (e.g., at \(x = 0\) or other \(x\) - values), it will intersect the graph more than once. So it is not a function.

Step3: Analyze Top - Right Graph

For the top - right graph, when we apply the vertical line test, any vertical line will intersect the graph at most once. So it represents a function.

Step4: Analyze Bottom - Left Graph

For the bottom - left graph (a straight line, likely a linear function \(y=mx + b\)), any vertical line will intersect the graph exactly once. So it represents a function.

Step5: Analyze Bottom - Right Graph

For the bottom - right graph (a parabola opening horizontally), a vertical line (e.g., \(x = 0\)) will intersect the graph more than once. So it is not a function.

Answer:

The top - right graph and the bottom - left graph represent functions. (In terms of the checkboxes, the checkbox for the top - right graph and the checkbox for the bottom - left graph should be selected.)