Question

In the graph of the square root function y=3squareroot of x-7+2, what are the coordinates of the pint farthest to the left?
the x-coordinate is _____
the y=coordinate is________

Answer 1

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.