Is This Graph a Function? Apply the Vertical Line Test

Function Testing with Linear Graphs

Is the given graph a function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the given graph a function?
00:05 The definition of a function is that for each X value there is one Y value
00:08 Let's check the graph values in the table to determine if it's a function
00:25 We can see that for each X value there is one Y value, therefore it's a function
00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Is the given graph a function?

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2

Step-by-step solution

To determine if the graph in question represents a function, we'll employ the Vertical Line Test. This test helps to ascertain whether each input value from the domain (x-values) is connected to a unique output value (y-values).

  • According to the Vertical Line Test, a graph represents a function if no vertical line can intersect the graph at more than one point.
  • In the provided diagram, the graph is a straight line.
  • Visual inspection shows that any vertical line drawn at any point along the x-axis intersects the line exactly once.
  • This indicates that for each x-value, there is a unique corresponding y-value. Therefore, the relationship depicted by the graph meets the criteria for a function.

Thus, the given graph correctly characterizes a function.
Therefore, the solution to the problem is Yes.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Vertical Line Test: Any vertical line intersects function graph once maximum
  • Technique: Draw imaginary vertical lines across entire graph domain
  • Check: Linear graphs always pass since no x-value repeats ✓

Common Mistakes

Avoid these frequent errors
  • Confusing vertical and horizontal line tests
    Don't use horizontal lines to test for functions = always wrong answer! Horizontal lines test for one-to-one functions, not basic functions. Always use vertical lines to determine if a graph represents a function.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the given graph is a function?

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FAQ

Everything you need to know about this question

What exactly is the Vertical Line Test?

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The Vertical Line Test checks if a graph represents a function. Draw imaginary vertical lines across the entire graph. If any vertical line touches the graph more than once, it's not a function.

Why do straight lines always pass the test?

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Straight lines (except vertical ones) always represent functions because they have a consistent slope. Each x-value corresponds to exactly one y-value, so no vertical line can intersect twice.

What would make a graph fail this test?

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Graphs that curve back on themselves fail the test. Examples include:

  • Circles
  • Sideways parabolas
  • Any graph where one x-value has multiple y-values

Do I need to check every possible vertical line?

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No! You just need to visually inspect the graph. If you can see any place where a vertical line would hit the graph twice, it fails the test.

What's the difference between a relation and a function?

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A relation is any set of ordered pairs (x,y). A function is a special relation where each input (x-value) has exactly one output (y-value). All functions are relations, but not all relations are functions!

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