Math Problem Statement

Specify the domain of the following function using interval notation.

Solution

To determine the domain of the function in the image, we need to observe the graph's behavior along the xx-axis.

  1. The graph starts at x=0x = 0 and moves to the right.
  2. There are no breaks or gaps in the graph as it moves rightward from x=0x = 0, implying that the function is continuous for all x0x \geq 0.

Thus, the domain of the function is all values of xx starting from 00 and extending indefinitely to the right. In interval notation, the domain is:

[0,)[0, \infty)

The correct choice is: [0, ∞).

Would you like more details or have any other questions?

Here are some related questions you might find helpful:

  1. How can I determine the range of a function from a graph?
  2. What does interval notation mean, and how is it used to describe domains?
  3. How do I recognize when a function is not defined at certain points (like holes or asymptotes)?
  4. How do increasing and decreasing intervals relate to the domain?
  5. How would the domain change if the graph had a vertical asymptote?

Tip: When finding the domain from a graph, always look at the horizontal extent (the xx-values) over which the graph exists.

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Math Problem Analysis

Mathematical Concepts

Functions
Graphs
Domain

Formulas

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Theorems

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Suitable Grade Level

Grades 8-10