Question

graphs, functions, and sequences
vertical line test
x graphs are shown below. click on the tabs to see them.
graph 1 graph 2 graph 3 graph 4 graph 5 graph 6
(graph of a relation with a coordinate plane, axes labeled x and y, and a graph)
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 graphs
explanation check

Explanation:

Step1: Recall Vertical Line Test

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

Step2: Analyze Graph 6

For Graph 6 (shown), draw a vertical line (e.g., \( x = 0 \)). This line intersects the graph at two points (top and bottom of the "V" at \( x = 0 \)). So, it fails the vertical line test.

Step3: Confirm Function Requirement

Since a function must have each \( x \)-value map to only one \( y \)-value, Graph 6 does not represent a function.

Answer:

Graph 6 does not represent a function (so the box for Graph 6 remains unchecked).