Question

six graphs are shown below. click on the tabs to see them.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6
check the box corresponding to each graph that represents a function.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6 none of the gr

Explanation:

To determine if a 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 Graph 2 (shown):

For any vertical line \( x = a \) (where \( a \) is a real number), we check how many times it intersects the graph:

• For \( x > 0 \): The graph has one segment (the upper line).
• For \( x = 0 \): The graph meets at a single point (the vertex).
• For \( x < 0 \): The graph has two segments, but a vertical line \( x = a \) (with \( a < 0 \)) will intersect only one of the two lines (since they are on opposite sides of the vertical line).

Thus, no vertical line intersects Graph 2 more than once. By the vertical line test, Graph 2 is a function.

(Note: Since only Graph 2 is shown, we analyze it. For other graphs, we would apply the same vertical line test, but they are not visible here. If we assume only Graph 2 is provided, it passes the vertical line test.)

Answer:

Graph 2 (check the box for Graph 2).