Math Problem Statement

Determine if the relation defines y as a function of x based on the given graph.

Solution

To determine if the given relation defines yy as a function of xx, we need to check whether every input value of xx has exactly one corresponding output value of yy.

The easiest way to verify this is by applying the vertical line test: if a vertical line drawn at any point along the graph intersects the graph in more than one place, then yy is not a function of xx.

Looking at the graph, no vertical line would intersect the graph at more than one point for any xx-value. Therefore, this relation does define yy as a function of xx.

Thus, the correct answer is:

  • Yes, this relation defines yy as a function of xx.

Would you like more clarification or further questions?

Here are 5 follow-up questions:

  1. How does the vertical line test work in identifying functions?
  2. Can this function be represented by an equation?
  3. What would happen if a vertical line intersected the graph at two points?
  4. How can you use the horizontal line test to determine if a function is one-to-one?
  5. What type of function (e.g., polynomial, trigonometric) does this graph likely represent?

Tip: A function passes the vertical line test if each xx-value has only one yy-value!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Graphing
Vertical Line Test

Formulas

-

Theorems

Vertical Line Test

Suitable Grade Level

Grades 9-12