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 of a piece - wise function with a line segment and a horizontal line segment)
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 3:

Looking at Graph 3, we observe the two parts of the graph. The line segment (from the left dot to the dot at \( x \approx 1 \)) and the horizontal segment (from the open circle at \( x \approx -1 \) to the right dot). If we apply the vertical line test, we check if any vertical line crosses the graph more than once. For \( x \)-values between the open circle and the intersection of the two segments, a vertical line would intersect both the slanted line and the horizontal line, meaning it fails the vertical line test. Thus, Graph 3 is not a function.

However, since the original question’s checkbox for Graph 3 is currently unchecked (and based on the vertical line test, it should remain unchecked), the correct status for Graph 3 is:

Answer:

\(\boldsymbol{\square}\) Graph 1 \(\boldsymbol{\checkmark}\) Graph 2 \(\boldsymbol{\square}\) Graph 3 \(\boldsymbol{\square}\) Graph 4 \(\boldsymbol{\square}\) Graph 5 \(\boldsymbol{\square}\) Graph 6 \(\boldsymbol{\square}\) None of the graphs

(Note: The final answer depends on all six graphs, but for Graph 3 specifically, it does not represent a function, so its checkbox remains unchecked.)