Math Problem Statement

Is it a function? Graphs and matching symbols: less than, equal, greater than.

Solution

To analyze your image and provide solutions, I'll break it into parts:

Part 1: "Is it a function?"

Graph (1):

To determine if the graph is a function, we apply the Vertical Line Test: if a vertical line intersects the graph at more than one point, it is not a function.
In this case, Graph (1) fails the Vertical Line Test, so it is not a function.

Graph (2):

For Graph (2), applying the Vertical Line Test, each vertical line intersects the graph at only one point.
Thus, Graph (2) is a function.


Part 2: "Match" section

This section involves comparing symbols or relationships ("less than," "equal," etc.) with their respective graphs or statements. However, the specific matches in the question aren't directly clear. Could you clarify how these matching symbols apply to the graphs, or do you want me to expand on the relationships for these?

Would you like more details, or clarification?


Expanded Learning:

  1. What is the Vertical Line Test and why does it work?
  2. How can we determine functions using algebra instead of graphs?
  3. Can a function fail the Vertical Line Test but still be a "relation"?
  4. What real-world phenomena can be represented by functions like Graph (2)?
  5. Why is it significant to classify a relation as a function?

Tip: Always test for a graph's functionality using the Vertical Line Test first—it’s a quick and reliable check!

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Math Problem Analysis

Mathematical Concepts

Vertical Line Test
Graph Interpretation
Functions and Relations

Formulas

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Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12