Math Problem Statement

Use graphing technology to find the domain of the function f(x) = √(x - 3) - 3.

Solution

The function given is:

f(x)=x33f(x) = \sqrt{x - 3} - 3

Finding the Domain

Since the function contains a square root, the expression inside the square root x3x - 3 must be non-negative (greater than or equal to 0).

x30x - 3 \geq 0

x3x \geq 3

Thus, the domain of the function is all real numbers xx such that x3x \geq 3.

Domain in Interval Notation:

[3,)[3, \infty)

This means the function is only defined for values starting from x=3x = 3 and going to infinity.


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Related Questions:

  1. What is the range of the function f(x)=x33f(x) = \sqrt{x - 3} - 3?
  2. How do square root functions behave for negative inputs?
  3. How do you determine domain for more complex functions with multiple constraints?
  4. What changes if the function were f(x)=3x3f(x) = \sqrt{3 - x} - 3?
  5. How does a graphing calculator verify the domain of a function?

Tip: When working with square roots, always start by ensuring the expression inside the radical is non-negative to find the domain.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Square Roots
Domain

Formulas

x - 3 ≥ 0

Theorems

Square Root Property

Suitable Grade Level

Grades 9-12