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________

1 answer

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.