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

1 answer

The function given is \( y = \sqrt{3x - 7} + 2 \). To find the coordinates of the point farthest to the left, we need to determine where the square root function is defined, as the square root is only defined for non-negative values.

We set the expression under the square root greater than or equal to zero:

\[ 3x - 7 \geq 0 \]

Solving this inequality:

\[ 3x \geq 7 \ x \geq \frac{7}{3} \]

The function is defined for \( x \geq \frac{7}{3} \). The point farthest to the left on the graph occurs at this value of \( x \).

Now, we can find the corresponding \( y \)-coordinate by substituting \( x = \frac{7}{3} \) into the function:

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

Thus, the point farthest to the left is:

\[ \left( \frac{7}{3}, 2 \right) \]

In summary, the coordinates are:

  • The x-coordinate is \( \frac{7}{3} \).
  • The y-coordinate is \( 2 \).