What effect does translating the radical function $$ k(x) = \sqrt{x} $$ vertically downward by 3 units have on its graph? Provide the new equation.

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To translate the radical function $$ k(x) = \sqrt{x} $$ vertically downward by 3 units, we need to subtract 3 from the function.

The general rule for vertical translations is:
- If you want to translate a function $$ f(x) $$ downward by $$ c $$ units, the new function will be $$ f(x) - c $$.

In this case, we have:
- Original function: $$ k(x) = \sqrt{x} $$
- Translation downward by 3 units: $$ k(x) - 3 $$

Thus, the new equation after the vertical translation is:
$$
k(x) = \sqrt{x} - 3
$$

This means that every point on the graph of $$ k(x) = \sqrt{x} $$ will move down by 3 units. The effect on the graph is that it will maintain its shape but will be positioned lower on the coordinate plane.
Translating the function $$ k(x) = \sqrt{x} $$ downward by 3 units changes its equation to $$ k(x) = \sqrt{x} - 3 $$. This moves the entire graph down by 3 units without altering its shape.

What effect does translating the radical function vertically downward by 3 units have on its graph? Provide the new equation.

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