Practice Problems for Precalculus Final Exam – Step-by-Step Guidance

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

Background

Topic: Functions and Graphs

This question is testing your ability to recognize whether a given graph represents a function. In precalculus, a function is a relation in which each input (x-value) corresponds to exactly one output (y-value).

Key Terms:

• 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, it is not 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 does not represent a function.

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

4. Pay attention to open and closed circles, as these indicate whether endpoints are included or excluded.

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 a vertical line can 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 fails the test.