Math Problem Statement

What is the domain of the graph shown?

Solution

The graph you uploaded represents a function that is defined for values of xx starting from 5-5 and extending to positive infinity. The graph shows an open circle at x=5x = -5, indicating that the function is not defined at that specific value, but is defined for all values greater than 5-5.

Thus, the domain of the graph is x5x \geq -5, which corresponds to the third option: 5x<-5 \leq x < \infty.

Would you like further clarification on this? Or do you have any additional questions?

Here are 5 related questions to consider:

  1. How do open and closed circles in a graph affect the domain and range of a function?
  2. What is the difference between a domain and a range of a function?
  3. How do you identify the domain of a function from its graph?
  4. Can the domain of a graph include negative values?
  5. What is the significance of infinity in describing the domain of a function?

Tip: Always pay attention to whether the graph has open or closed circles at boundary points, as this will tell you whether those points are included in the domain.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Inequalities

Formulas

Domain of a function: The set of all possible input values (x-values) for which the function is defined.

Theorems

A function's domain is determined by examining its graph, ensuring it includes all x-values for which the function is valid.

Suitable Grade Level

Grades 8-10