To find the domain of the function \( f(x) = \sqrt{x + 1} \), we need to identify the values of \( x \) for which the function is defined. Since we are dealing with a square root function, the expression inside the square root must be non-negative:
\[ x + 1 \geq 0 \]
Solving this inequality:
\[ x \geq -1 \]
Thus, the function \( f(x) = \sqrt{x + 1} \) is defined for all \( x \) greater than or equal to \(-1\).
In interval notation, the domain of the function is:
\[ [-1, \infty) \]
Using graphing technology, you would visually inspect the graph of \( f(x) \) and confirm that the function exists and starts from the point \( (-1, 0) \) and continues to the right indefinitely.