To find the ordered pair of the endpoint in the standard form of the square root function \( y = \sqrt{5x - 4} - 1 \), we first identify the expression under the square root.
The expression inside the square root, \( 5x - 4 \), must be greater than or equal to zero for the function to be defined. So, we set up the inequality:
\[ 5x - 4 \geq 0 \]
Solving for \( x \):
\[ 5x \geq 4 \quad \Rightarrow \quad x \geq \frac{4}{5} \]
At \( x = \frac{4}{5} \), we calculate \( y \):
\[ y = \sqrt{5 \left( \frac{4}{5} \right) - 4} - 1 = \sqrt{4 - 4} - 1 = \sqrt{0} - 1 = 0 - 1 = -1 \]
Thus, the ordered pair (endpoint) is:
\[ \left( \frac{4}{5}, -1 \right) \]
This is the endpoint of the function as the square root function starts from this point and extends to the right.
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