Q7–Q10. Determine whether the graph is a graph of a function of x.

Background

Topic: Functions and Graphs

These questions test your understanding of what qualifies as a function based on its graph. In calculus, a function is a relation where each input (x-value) corresponds to exactly one output (y-value). The most common graphical test for this is the "vertical line test."

Key Terms and Concepts:

• Function: A relation in which every x-value has only one y-value.

• Vertical Line Test: If any vertical line crosses the graph more than once, the graph does not represent a function.

Step-by-Step Guidance

1. Examine the graph carefully. For each graph, imagine drawing vertical lines at various x-values.

2. Ask yourself: Does any vertical line intersect the graph at more than one point? If so, the graph is not a function.

3. If every vertical line crosses the graph at most once, then the graph is a function.

4. Apply this reasoning to each graph provided. For example, a straight line or a parabola typically passes the vertical line test, while a circle does not.

5. Review the images below and use the vertical line test to decide for each graph.

Try solving on your own before revealing the answer!