Question

determine whether the graph shown is the graph of a function.

select the correct answer below:

the graph represents a function.

Explanation:

Understand the definition of a function

A relation represented by a graph is a function if and only if each input \(x\) corresponds to exactly one output \(y\).

Apply the vertical line test

To determine if a graph represents a function, we use the Vertical Line Test. If any vertical line intersects the graph at more than one point, the graph does not represent a function. If every vertical line intersects the graph at most once, it represents a function.

Analyze the given graph

The given graph is a straight line with a steep positive slope. It passes through the y-axis near \((0, 1)\) and continues infinitely in both directions.

Evaluate vertical line intersections

Any vertical line drawn of the form \(x = c\) will intersect this straight line exactly once. No vertical line can intersect this line at more than one point. Therefore, the graph passes the vertical line test.

Formulate the final conclusion

Since the graph passes the vertical line test, it represents a function.

Answer:

• The graph represents a function. (Correct answer)
• The graph does not represent a function.