Final Answer:
The correct test to determine if a graph represents a function is the Vertical Line Test (option b).
Step-by-step explanation:
The Vertical Line Test is a powerful tool in assessing whether a given graph represents a function. To apply this test, visualize each vertical line crossing the graph. If any vertical line intersects the graph at more than one point, the graph fails the Vertical Line Test, indicating that it does not represent a function. On the other hand, if every vertical line crosses the graph at most once, the graph satisfies the Vertical Line Test, confirming that it represents a function (option b).
The reasoning behind the Vertical Line Test lies in the definition of a function, where each input (x-value) should correspond to exactly one output (y-value). By employing vertical lines, we can easily evaluate whether a particular x-value maps to a unique y-value. This intuitive test is a valuable tool for students and mathematicians alike when examining graphs and determining their functional nature.
In summary, the Vertical Line Test is a straightforward yet effective method for verifying if a graph represents a function. Its simplicity and visual nature make it a widely used technique in introductory calculus and algebra courses.