To transform the function $y = \sqrt{x} - 3$, let's break down the transformation steps:

1. Starting Function:

• The basic function is $y = \sqrt{x}$.
• This function represents the square root of $x$, which is a curve starting from the origin (0,0) and increasing slowly as $x$ increases.

2. Vertical Shift:

• The transformation $y = \sqrt{x} - 3$ indicates a vertical shift.
• Specifically, subtracting 3 shifts the entire graph downward by 3 units.

Summary of Transformation:

• The graph of $y = \sqrt{x}$ is shifted down by 3 units to get the graph of $y = \sqrt{x} - 3$.

Resulting Graph:

• The new graph still starts at $x = 0$, but the starting point is now at $(0, -3)$.
• The curve follows the same shape as $y = \sqrt{x}$ but is shifted downward.

Would you like more details or have any questions?

Related Questions:

1. How would you transform $y = \sqrt{x} + 2$?
2. What would the graph of $y = \sqrt{x + 3}$ look like?
3. How does the function $y = -\sqrt{x}$ differ from $y = \sqrt{x}$?
4. What are the domain and range of the function $y = \sqrt{x} - 3$?
5. How do horizontal shifts affect the graph of $y = \sqrt{x}$?

Tip:

Always check the domain of the original function before applying transformations to ensure the results are valid over the intended range.