The image shows a question asking for the domain and range of the function $f(x) = \sqrt{x - 4}$.

Explanation:

1. Domain: The domain of the function $f(x) = \sqrt{x - 4}$ consists of all values of $x$ for which the expression under the square root is non-negative (because the square root of a negative number is not a real number). Therefore, we set $x - 4 \geq 0$, which gives $x \geq 4$. So, the domain is $[4, \infty)$.

2. Range: The range of the function is determined by the output values of $f(x)$. Since the square root function produces non-negative outputs, and the smallest value inside the square root is 0 (when $x = 4$), the range of $f(x) = \sqrt{x - 4}$ is $[0, \infty)$.

Answer:

• The correct answer, as indicated in the image, is Option A:
  • Domain: $[4, \infty)$
  • Range: $[0, \infty)$

Would you like further details on the function's domain and range, or do you have any other questions?

Related Questions:

1. How would the domain and range change if the function were $f(x) = \sqrt{4 - x}$?
2. What is the domain of the function $f(x) = \frac{1}{\sqrt{x - 4}}$?
3. How do you find the range of a quadratic function?
4. What is the difference between the domain and range of a function?
5. How would you graph the function $f(x) = \sqrt{x - 4}$?

Tip:

When determining the domain of a function involving a square root, always consider the expression under the root and set it greater than or equal to zero to find the permissible values of $x$.