Questions: Write the function whose graph is the graph of y=sqrt(x), but is translated 7 units downward.

Transcript text: Write the function whose graph is the graph of $y=\sqrt{x}$, but is translated 7 units downward.

Solution

Solution Steps

To translate the graph of the function $ y = \sqrt{x} $ 7 units downward, we need to subtract 7 from the function. This means the new function will be $ y = \sqrt{x} - 7 $.

Step 1: Understand the Original Function

The original function given is $ y = \sqrt{x} $. This is the graph of the square root function, which starts at the origin $(0,0)$ and increases as $ x $ increases.

Step 2: Apply the Translation

To translate a function downward, we subtract a constant from the function. In this case, we need to translate the graph 7 units downward. Therefore, we subtract 7 from the original function:

\[ y = \sqrt{x} - 7 \]