Math Problem Statement
Is this a function?
Solution
The image shows a graph of a circle in the plane. To determine if the given relation is a function, we can apply the Vertical Line Test. This test states that a graph represents a function if no vertical line intersects the graph more than once.
In the image, we see a vertical dashed line at , which intersects the circle at two points. Since the vertical line crosses the graph more than once, this means that for some values of , there are multiple values of .
Thus, this graph does not represent a function because it fails the vertical line test.
Would you like more details on this? Here are some related questions you might find interesting:
- What is the vertical line test and why does it determine if a graph is a function?
- How can you tell if a relation is a function by looking at its equation?
- What is the equation of a circle and how does it differ from a function?
- How can we modify this graph so that it represents a function?
- Are there special cases where a relation can still be considered a function even if the vertical line test fails?
Tip: A function must assign only one output value for each input value, which is why passing the vertical line test is crucial for determining whether a graph represents a function.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Functions
Graph Theory
Formulas
-
Theorems
Vertical Line Test
Suitable Grade Level
Grades 8-10
Related Recommendation
Understanding Functions: Analyzing Graphs with the Vertical Line Test
Is the Relation Represented by a Circle a Function?
Determine If a Graph Represents a Function Using the Vertical Line Test
Determining if a Graph Represents a Function Using the Vertical Line Test
Vertical Line Test: Determining Functions from Graphs