Here is the graph of $f(x) = \sqrt{x + 4} - 3$.

Graph Description:

• The graph starts at the point $(-4, -3)$ and continues to rise as $x$ increases, indicating an upward trend.
• It is a transformed square root function with a leftward shift and downward shift. This causes the graph to start lower on the y-axis and begin at $x = -4$.
• Key points such as $(-4, -3)$, $(0, -1)$, and $(5, 0)$ illustrate its progression, giving a smooth, curved increase as $x$ moves rightward.

Would you like more details on transformations or how to derive similar functions?

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Here are 5 related questions to deepen understanding:

1. What is the effect of changing the -3 in $\sqrt{x + 4} - 3$ to a different constant?
2. How would the graph change if the function was $f(x) = -\sqrt{x + 4} - 3$?
3. How do we determine the range of functions with transformations like square roots?
4. Can this function have an inverse? If so, what would it look like?
5. How do transformations impact the domain of functions involving square roots?

Tip: When analyzing transformations, always check how the "inside" and "outside" operations on the function affect the graph, as they shift or stretch it accordingly.