Analyzing Graphs to Determine if They Represent Functions

Q6. Determine if the graph represents the graph of a function.

Background

Topic: Functions and Graphs

This question tests your understanding of what qualifies as a function in mathematics, specifically by analyzing graphs. A function is a relation in which each input (x-value) corresponds to exactly one output (y-value).

Key Terms and Concepts:

• Function: A relation where each input has only one output.

• Vertical Line Test: A graphical method to determine if a curve is a function. 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 and imagine drawing vertical lines at various points along the x-axis.

2. For each vertical line, check if it intersects the graph at more than one point. If it does, the graph fails the vertical line test and is not a function.

3. If every vertical line intersects the graph at most once, then the graph passes the vertical line test and represents a function.

4. Pay attention to open and closed circles, which indicate whether endpoints are included or excluded. This can affect whether the graph is a function at those points.

Try solving on your own before revealing the answer!

Final Answer:

Graphs 1, 2, 3, and 4 represent functions because they pass the vertical line test. Graph 5 does not represent a function because some vertical lines intersect the spiral at multiple points.

The vertical line test is a quick way to check if a graph is a function: if any vertical line crosses the graph more than once, it is not a function.