Question

home work - determine if each graph shows a function and explain how you decided/

Explanation:

Step1: Recall vertical line test rule

A graph represents a function if any vertical line drawn intersects the graph at at most one point.

Step2: Analyze Graph 44

Draw vertical lines; each intersects once.
Conclusion: Passes vertical line test.

Step3: Analyze Graph 48

Draw vertical lines; some intersect multiple times.
Conclusion: Fails vertical line test.

Step4: Analyze Graph 63

Draw vertical lines; each intersects at most once.
Conclusion: Passes vertical line test.

Step5: Analyze Graph 65

Draw vertical lines; each intersects at most once.
Conclusion: Passes vertical line test.

Step6: Analyze Graph 68

Draw vertical lines; each intersects at most once.
Conclusion: Passes vertical line test.

Answer:

1. Graph 44: Is a function. It passes the vertical line test (no vertical line intersects the graph more than once).
2. Graph 48: Is NOT a function. It fails the vertical line test (some vertical lines intersect the graph multiple times).
3. Graph 63: Is a function. It passes the vertical line test (no vertical line intersects the graph more than once).
4. Graph 65: Is a function. It passes the vertical line test (no vertical line intersects the graph more than once).
5. Graph 68: Is a function. It passes the vertical line test (no vertical line intersects the graph more than once).