Use graphing technology to find the range of the function f, of, x, equals, square root of, x, plus, 5, end square root, minus, 4, .f(x)=

To find the range of the function \( f(x) = \sqrt{x + 5} - 4 \), we first analyze the components of the function:

1. **Identify the domain**: The function includes a square root, which means the expression inside the radical must be non-negative:
\[
x + 5 \geq 0 \implies x \geq -5.
\]
Therefore, the domain of \( f(x) \) is \( x \in [-5, \infty) \).

2. **Behavior of the function**:
- When \( x = -5 \):
\[
f(-5) = \sqrt{-5 + 5} - 4 = \sqrt{0} - 4 = -4.
\]
- As \( x \) increases beyond -5, \( \sqrt{x + 5} \) also increases. Specifically, as \( x \to \infty \):
\[
f(x) \to \infty \text{ (since } \sqrt{x + 5} \text{ will approach infinity)}.
\]

3. **Combining the above observations**:
- The minimum value of \( f(x) \) occurs at \( x = -5 \), which is \( -4 \).
- As \( x \) increases, \( f(x) \) increases without bound.

Thus, the range of the function is:
\[
\text{Range of } f(x) = [-4, \infty).
\]

In summary:
- The minimum value of \( f(x) \) is -4, which occurs at the left endpoint of the domain.
- There is no upper bound on \( f(x) \) as \( x \) increases.
- Therefore, the final answer is:
\[
\text{Range} = [-4, \infty).
\]