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
(graph 4s coordinate plane graph: a curve opening downward, vertex at origin, intersecting x - axis at some points, etc.)
check the box corresponding to each graph that represents a function.
□ graph 1 □ graph 2 (checked) □ graph 3 □ graph 4 □ graph 5 □ graph 6 □ none of the

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 4:

Looking at Graph 4 (the parabola opening downward), we apply the vertical line test. For any vertical line \( x = a \) (where \( a \) is a real number), the line will intersect the graph at most once. This satisfies the vertical line test, so Graph 4 is a function.

Updating the Checkbox:

Since Graph 4 passes the vertical line test, we check its corresponding box.

Answer:

• Graph 1: Unchecked
• Graph 2: Checked (as given)
• Graph 3: Unchecked
• \(\boldsymbol{\text{Graph 4}}\): Checked
• Graph 5: Unchecked
• Graph 6: Unchecked
• None of the above: Unchecked

(Note: The final answer here reflects that Graph 4 should be checked. If the original problem required only identifying Graph 4, the answer is that Graph 4 represents a function and its box should be checked.)