The transformation of the graph of the parent function $y = \sqrt{x}$ for the function $y = \sqrt{x} + 7 + 5$ involves vertical and horizontal shifts. Let’s break down the transformation step by step:

The given function is:

$y = \sqrt{x} + 7 + 5$

This can be rewritten as:

$y = (\sqrt{x}) + 7 + 5 = \sqrt{x} + 12$

Analysis of the Transformation

1. Vertical Shift: The term $+12$ indicates a vertical shift. The graph of the parent function $y = \sqrt{x}$ is shifted 12 units up. This is because adding a constant outside the square root function affects the vertical position of the graph.

2. Horizontal Shift: There is no horizontal shift in this case because there is no transformation inside the square root (no addition or subtraction affecting the $x$ term directly).

Final Description

The graph of $y = \sqrt{x}$ is shifted 12 units up.

If you originally saw the phrase "shifted 7 units" and "5 units" in your question, it may have been referring to an error. The correct transformation for this function is 12 units up and no horizontal shift.

Would you like to explore this further or check another problem?

Related Questions:

1. What would be the transformation if the function were $y = \sqrt{x - 3} + 7$?
2. How would the graph shift if the function were $y = -\sqrt{x} + 4$?
3. If the function were $y = 2\sqrt{x} - 5$, what would the transformations be?
4. How does a horizontal shift differ from a vertical shift in terms of function notation?
5. What would the domain and range of $y = \sqrt{x} + 12$ be?

Tip:

Always check if a transformation is applied inside or outside the function