Question

graph the function.
$y = -\sqrt{x - 1}$
click to plot points on the graph. plot the endpoint first.

Explanation:

Step1: Find the domain endpoint

The expression under the square root must be non-negative:
$x - 1 \geq 0 \implies x \geq 1$
Substitute $x=1$ into the function:
$y = -\sqrt{1 - 1} = 0$
Endpoint: $(1, 0)$

Step2: Calculate additional points

Choose $x=2$:
$y = -\sqrt{2 - 1} = -1$
Point: $(2, -1)$

Choose $x=5$:
$y = -\sqrt{5 - 1} = -\sqrt{4} = -2$
Point: $(5, -2)$

Choose $x=10$:
$y = -\sqrt{10 - 1} = -\sqrt{9} = -3$
Point: $(10, -3)$

Step3: Plot and connect points

Plot the endpoint $(1,0)$ first, then plot $(2,-1)$, $(5,-2)$, $(10,-3)$, and draw a smooth curve extending to the right (since $x$ increases indefinitely, $y$ decreases downward indefinitely).

Answer:

The graph has an endpoint at $(1, 0)$, passes through $(2, -1)$, $(5, -2)$, $(10, -3)$, and is a downward-opening square root curve defined for $x \geq 1$.