Question

graph the function below by dragging the points.
g(x)=\sqrt{x - 1}
show your work here
draw

Explanation:

Step1: Find the domain

For the function $g(x)=\sqrt{x - 1}$, the expression under the square - root must be non - negative. So, $x-1\geq0$, which gives $x\geq1$.

Step2: Find some key points

When $x = 1$, $g(1)=\sqrt{1 - 1}=0$.
When $x=2$, $g(2)=\sqrt{2 - 1}=1$.
When $x = 5$, $g(5)=\sqrt{5 - 1}=2$.

Step3: Analyze the shape

The function $y = \sqrt{x}$ is a square - root function. The function $g(x)=\sqrt{x - 1}$ is a horizontal shift of $y=\sqrt{x}$ one unit to the right. As $x$ increases, $g(x)$ also increases, but at a decreasing rate.

Answer:

Plot the points $(1,0)$, $(2,1)$, $(5,2)$ and draw a smooth curve starting from the point $(1,0)$ and increasing as $x$ increases for $x\geq1$.