Question

graph the function. f(x)=\sqrt{x - 1}-6. plot four points on the graph of the function: the leftmost point and three additional points. then click on the graph - a - function button.

Explanation:

Step1: Find the domain

For the function $f(x)=\sqrt{x - 1}-6$, the expression under the square - root must be non - negative. So $x-1\geq0$, which gives $x\geq1$. The leftmost point occurs when $x = 1$.

Step2: Calculate the leftmost point

When $x = 1$, $f(1)=\sqrt{1 - 1}-6=-6$. So the leftmost point is $(1,-6)$.

Step3: Choose additional $x$ values

Let's choose $x = 2$, $x = 5$, and $x = 10$.
When $x = 2$, $f(2)=\sqrt{2 - 1}-6=1 - 6=-5$.
When $x = 5$, $f(5)=\sqrt{5 - 1}-6=2 - 6=-4$.
When $x = 10$, $f(10)=\sqrt{10 - 1}-6=3 - 6=-3$.
So the three additional points are $(2,-5)$, $(5,-4)$, $(10,-3)$.

Answer:

The four points are $(1,-6)$, $(2,-5)$, $(5,-4)$, $(10,-3)$