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What is the Vertical Line Test for Functions?

question
Practice Problems


Problem 1) Does the graph below represent a function or a relation?
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Vertical Line test practice graph

Problem 2) Does the graph below represent a function or a relation?
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Vertical Line test practice graph

Problem 3) Does the graph below represent a function or a relation?
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Vertical Line test practice graph

Problem 4) Does the graph below represent a function or a relation?
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Answer : No. No matter where you try to draw a vertical line, it only hits the graph once so this is a function
Be careful at x =2. The point (2,1) is not filled in, indicating that the graph does not include the point (2,1). However, notice that (2,2) is completely filled in, because that point is included in the graph.
Vertical Line test practice graph

Problem 5) Does the graph below represent a function or a relation? (look carefully, this graph is slightly different from the prior problem's graph)
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Answer : Yes. Unlike problem 3, in this case, the point (2,1) is filled in and is,therefore, included in the graph.
As you can see, that one point makes all the difference. this is not a function
Vertical Line test practice graph

Problem 6) Does the graph below represent a function or a relation? (look carefully, this graph is slightly different from the prior problem's graph)
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Answer : Yes. This is not a function . In fact, circles, in general, are not functions.
Vertical Line test practice graph

Problem 7) Does the graph below represent a function or a relation? (look carefully, this graph is slightly different from the prior problem's graph)
Step 1
Ask yourself:
"Can I draw a vertical line (anywhere) that will hit the graph two times ?"
Answer
Answer : No. This is a function .
Vertical Line test practice graph
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