To solve this problem, let's first break down the original function and what happens when we shift it.

The given function is:

$f(x) = -2\sqrt{x}$

This function represents a transformed square root function that is reflected vertically (due to the negative sign), stretched by a factor of 2, and rooted at $x = 0$.

The goal is to shift the graph right by 1 unit.

In general, to shift a function $f(x)$ horizontally:

• A shift right by $h$ units is achieved by replacing $x$ with $x - h$.
• A shift left by $h$ units is achieved by replacing $x$ with $x + h$.

Since we are asked to shift the graph to the right by 1 unit, the equation for the new function $g(x)$ will be:

$g(x) = -2\sqrt{x - 1}$

Explanation:

• The term $x - 1$ inside the square root shifts the graph of the original function $f(x)$ to the right by 1 unit.
• The rest of the function remains the same, with the vertical reflection and the stretch by 2.

Thus, the equation of the shifted function is:

$g(x) = -2\sqrt{x - 1}$

Would you like a more detailed explanation of this transformation or further clarification?

Here are some follow-up questions for deeper understanding:

1. How would you shift the graph left by 2 units instead of right by 1?
2. What would happen if the constant outside the square root was positive instead of negative?
3. How would the graph change if we also wanted to shift it upward by 3 units?
4. Can you describe how the graph would look if we applied a vertical compression by a factor of 0.5?
5. What does the domain of the new function $g(x)$ look like after the horizontal shift?

Tip: Shifting functions horizontally is always related to modifying the variable $x$ inside the function, while vertical shifts involve adding/subtracting outside of the main function.