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 \( 2 \).
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