Question

What is the ordered pair of the endpoint in the standard form of a square root function y=5x−4−−−−−√−1
?(1 point)

Answer 1

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.