Question

In the graph of the square root function y=3√x−7−−−−−+2
, what are the coordinates of the point farthest to the left?(1 point)
The x-coordinate is _.

The y-coordinate is _.

Answer 1

To determine the coordinates of the point farthest to the left for the function \( y = 3\sqrt{x - 7} + 2 \), we first identify the domain of the function. The square root function is only defined for non-negative values, so we need to find the value of \( x \) such that \( x - 7 \geq 0 \).

Solving \( x - 7 \geq 0 \):
\[
x \geq 7
\]

This means that the function is defined for \( x \) values starting from \( 7 \) and going to positive infinity. The farthest point to the left on the graph of the function occurs at the left endpoint of this domain.

Thus, the farthest point to the left is at \( x = 7 \).

Next, we substitute \( x = 7 \) back into the function to find the corresponding \( y \)-coordinate.

\[
y = 3\sqrt{7 - 7} + 2 = 3\sqrt{0} + 2 = 0 + 2 = 2
\]

So the coordinates of the point farthest to the left are \( (7, 2) \).

The x-coordinate is **7**.
The y-coordinate is **2**.