Determine Function: Vertical Line Validation on Given Graph

Q: What exactly is the vertical line test?

The vertical line test is a visual method to check if a graph represents a function. Imagine drawing vertical lines across the entire graph - if any vertical line touches the graph at more than one point, it's not a function!

Q: Why does this graph fail the vertical line test?

Looking at $ x = 3 $, there's a vertical line segment that goes from $ y = -3 $ to $ y = 3 $. This means one x-value has multiple y-values, which violates the function definition.

Q: Can a graph have vertical parts and still be a function?

No! Any vertical line, segment, or curve in a graph automatically means it's not a function. Functions must pass the vertical line test everywhere on their domain.

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

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

Q: How do I remember which line test to use?

Think 'V for Vertical, F for Function'! Use vertical lines to test if something is a function. Horizontal lines test for one-to-one functions (invertible functions).

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's find out if the graph is a function.

00:07 A function means each x-value has exactly one y-value.

00:12 Here, it looks like one x-value has multiple y-values.

00:17 So, this graph is not a function.

00:21 Remember, a line parallel to the y-axis is not a function.

00:25 And that's how we solve this 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?

2

Step-by-step solution

To determine whether the graph represents a function, we apply the Vertical Line Test. Here are the steps we follow:

Step 1: Visualize placing a vertical line across various parts of the graph.
Step 2: Check if the vertical line intersects the graph at more than one point at any given position.

Step 1: On evaluating the given graph carefully, there is a notable presence of a vertical line passing through multiple y-values. Specifically, the vertical line goes from $y = -3$ to $y = 3$ at $x = 3$ .

Step 2: Since this vertical line at $x = 3$ intersects the graph at an infinite number of points, it fails the Vertical Line Test.

Therefore, the graph does not represent a function. According to our analysis and the Vertical Line Test, the correct answer is No.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic

Function Definition: Each input x-value has exactly one output y-value
Vertical Line Test: Draw imaginary vertical lines across entire graph domain
Check: If any vertical line intersects graph more than once, not a function ✓

Common Mistakes

Avoid these frequent errors

Confusing vertical and horizontal line tests
Don't use horizontal lines to test if something is a function = wrong conclusion! Horizontal lines test if a function is one-to-one, not if a relation is a function. Always use vertical lines to determine if a graph represents a function.

Practice Quiz

Test your knowledge with interactive questions

Is the given graph a function?

FAQ

Everything you need to know about this question

What exactly is the vertical line test?

+

The vertical line test is a visual method to check if a graph represents a function. Imagine drawing vertical lines across the entire graph - if any vertical line touches the graph at more than one point, it's not a function!

Why does this graph fail the vertical line test?

+

Looking at $x = 3$ , there's a vertical line segment that goes from $y = -3$ to $y = 3$ . This means one x-value has multiple y-values, which violates the function definition.

Can a graph have vertical parts and still be a function?

+

No! Any vertical line, segment, or curve in a graph automatically means it's not a function. Functions must pass the vertical line test everywhere on their domain.

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

+

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

How do I remember which line test to use?

+

Think 'V for Vertical, F for Function'! Use vertical lines to test if something is a function. Horizontal lines test for one-to-one functions (invertible functions).

What if the vertical line just touches at one point?

+

That's perfectly fine! A vertical line can touch the graph at exactly one point and it still passes the test. The problem only occurs when it intersects at two or more points.

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Determine Function: Vertical Line Validation on Given Graph

Vertical Line Test with Graph Analysis

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