https://file.aiquickdraw.com/mathbot/file/1726768870567x1q95qmo.jpg

The function given is \( k(x) = \sqrt{x + 4} \).

### To determine the range:
1. **Domain considerations**: The square root function, \( \sqrt{x} \), is defined only for \( x \geq 0 \). Therefore, we need:
   \[
   x + 4 \geq 0 \implies x \geq -4
   \]
   So, the domain of \( k(x) \) is \( x \geq -4 \).

2. **Range determination**: 
   - Since the square root function \( \sqrt{x} \) always outputs non-negative values, we know that \( k(x) \geq 0 \).
   - The minimum value occurs when \( x = -4 \), which gives \( k(-4) = \sqrt{-4 + 4} = \sqrt{0} = 0 \).
   - As \( x \to \infty \), \( k(x) \) increases without bound, meaning \( k(x) \to \infty \).

Thus, the range of the function is:
\[
\boxed{[0, \infty)}
\]

Let me know if you'd like more details or have any questions! Here are some related questions you might find useful:

1. How do you determine the domain of a square root function?
2. What happens to the range if the function was \( \sqrt{x - 4} \) instead?
3. How does the graph of \( k(x) = \sqrt{x + 4} \) look compared to \( \sqrt{x} \)?
4. What would the range be if the function was \( k(x) = -\sqrt{x + 4} \)?
5. How can the range be affected by adding constants outside the square root, such as \( k(x) = \sqrt{x + 4} + 2 \)?

**Tip**: The range of a square root function depends mainly on the fact that the output of the square root is always non-negative unless negated.

For the function k(x) = √(x + 4), determine the range.

Learn how to determine the range for the function k(x) = √(x + 4). This problem explains the domain and range for square root functions. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation