To find the coordinates of the point farthest to the left on the graph of the function \( y = 3\sqrt{x - 7} + 2 \), we first need to determine the domain of the function.
The square root function \( \sqrt{x - 7} \) is defined when the expression inside the square root is non-negative. Therefore, we need:
\[ x - 7 \geq 0 \]
This simplifies to:
\[ x \geq 7 \]
The leftmost point in the domain occurs at \( x = 7 \).
Now, substituting \( x = 7 \) back into the function to find the corresponding \( y \)-coordinate:
\[ y = 3\sqrt{7 - 7} + 2 = 3\sqrt{0} + 2 = 0 + 2 = 2 \]
Thus, the coordinates of the point farthest to the left on the graph are:
- The x-coordinate is \( 7 \).
- The y-coordinate is \( 2 \).
In summary:
- The x-coordinate is 7.
- The y-coordinate is 2.
So the answer is:
- The x-coordinate is 7.
- The y-coordinate is 2.