Math Problem Statement

In alternate notation

Solution

The graph shown is a curve that appears to be continuous. To determine the domain of the graph, we need to identify the set of all possible xx-values for which the graph is defined.

Analysis:

  • The graph starts from a point on the left, crosses the x-axis, continues upward, and then curves back downward to the right.
  • There don't appear to be any breaks, gaps, or undefined points in the curve along the x-axis.

Conclusion: The domain of the graph includes all real numbers, meaning that for every value of xx, there is a corresponding yy value on the graph. This can be written in interval notation as:

Domain=(,)\text{Domain} = (-\infty, \infty)

This indicates that the graph is defined for all xx-values.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

  1. What is the range of the given graph?
  2. How can the continuity of a graph be determined?
  3. What are some common types of functions with domains of all real numbers?
  4. How does the domain of a function change with vertical or horizontal shifts?
  5. What are the effects of restricting the domain of a function?

Tip: Always check the entire graph for any vertical asymptotes, holes, or other discontinuities when determining the domain.

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Math Problem Analysis

Mathematical Concepts

Graph Theory
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

High School