College Algebra Test 1 Review – Step-by-Step Guidance

Q15. Which of the two graphs below represents a function? Explain why.

Background

Topic: Functions and Graphs

This question tests your understanding of what it means for a graph to represent a function. In College Algebra, a function is a relation in which each input (x-value) has exactly one output (y-value).

Key Terms and Concepts:

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

• Vertical Line Test: A visual way to determine if a graph represents a function. If any vertical line crosses the graph more than once, the graph does not represent a function.

Step-by-Step Guidance

1. Recall the definition of a function: For every x-value, there should be only one corresponding y-value.

2. Apply the vertical line test: Imagine drawing vertical lines (parallel to the y-axis) across the graph.

3. Observe the graph: If any vertical line touches the graph at more than one point, then the graph fails the vertical line test.

4. Analyze the provided graph: Look for places where a vertical line would intersect the curve more than once.

5. Decide if the graph passes or fails the vertical line test, but do not state the final conclusion yet.

Try solving on your own before revealing the answer!

Final Answer:

The graph shown does not represent a function. This is because there are vertical lines (for example, near the left side of the graph) that intersect the curve at more than one point. Therefore, for some x-values, there are multiple corresponding y-values, which violates the definition of a function.

The vertical line test confirms this: since some vertical lines cross the graph twice, it is not a function.