Let's analyze the transformations from the given functions:

1. The original function is $f(x) = \sqrt{x}$.
2. The transformed function is $g(x) = 2\sqrt{x+4} - 7$.

Now, let's break down the transformations:

• Vertical Stretch: The coefficient 2 in front of $\sqrt{x+4}$ stretches the graph vertically. This is a vertical stretch.
• Horizontal Shift: The expression $\sqrt{x+4}$ indicates a horizontal shift. Since it is $x+4$, the graph is shifted 4 units to the left.
• Vertical Shift: The constant $-7$ at the end subtracts 7 from the entire function, which shifts the graph 7 units down.

Conclusion:

The three transformations are:

1. Vertical Stretch
2. Horizontal Shift Left 4 units
3. Vertical Shift Down 7

Would you like a detailed explanation of any part of this transformation?

Here are 5 questions to deepen your understanding:

1. How does changing the coefficient of the square root affect the graph of the function?
2. What would happen if the transformation was $\sqrt{x-4}$ instead of $\sqrt{x+4}$?
3. How would the graph be different if the vertical shift was positive instead of negative?
4. What is the difference between a vertical stretch and a vertical compression?
5. How do you identify horizontal transformations based on the expression inside the square root?

Tip: Always remember that transformations inside the square root affect the graph horizontally, while transformations outside affect it vertically.