Question

warm up
determine whether each
graph represents a function.
explain your reasoning.
1.

2.

3.

Explanation:

To determine if a graph represents a function, use the Vertical Line Test: any vertical line drawn on the graph should intersect the graph at most once.

1. For the first graph (parabola opening upward): Every vertical line intersects the graph at exactly one point, so it passes the test.
2. For the second graph: There exists at least one vertical line that intersects the graph at two points, so it fails the test.
3. For the third graph: Every vertical line intersects the graph at exactly one point, so it passes the test.

Answer:

1. This graph represents a function. It passes the Vertical Line Test, as no vertical line intersects the graph more than once.
2. This graph does NOT represent a function. It fails the Vertical Line Test, as some vertical lines intersect the graph at two points.
3. This graph represents a function. It passes the Vertical Line Test, as no vertical line intersects the graph more than once.