Math Problem Statement

What is the domain of the square root function graphed below?

Solution

To determine the domain of the square root function graphed, we observe where the graph exists along the x-axis, since the domain refers to the set of all possible x-values for which the function is defined.

From the graph:

  • The function starts at x=1x = 1 and extends to the right.
  • There are no parts of the function graphed for x<1x < 1.

Therefore, the domain of this square root function is: x1x \geq 1

The correct answer is: x1x \geq 1.

Would you like more details or have any questions?

Here are some related questions:

  1. What is the range of this square root function?
  2. How do you determine the domain of a square root function in general?
  3. What transformations could shift this square root graph horizontally?
  4. How does the domain change if we reflect the graph across the y-axis?
  5. What happens to the domain if we consider a square root function with a vertical stretch?

Tip: When determining the domain of a square root function, remember that the expression inside the square root must be non-negative (greater than or equal to zero).

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Math Problem Analysis

Mathematical Concepts

Functions
Domain of Square Root Functions
Graphs

Formulas

The function inside the square root must be non-negative, i.e., x - 1 ≥ 0

Theorems

Domain Rule for Square Root Functions

Suitable Grade Level

Grades 9-11