Question

use translations to graph the given function.
$g(x) = \sqrt{x - 2}$

Explanation:

Step1: Identify parent function

Parent function: $f(x)=\sqrt{x}$

Step2: Determine translation type

Horizontal shift right by 2 units: $g(x)=f(x-2)$

Step3: Plot key points of parent

Key points of $f(x)$: $(0,0), (1,1), (4,2), (9,3)$

Step4: Apply translation to points

Shift each x-coordinate +2:
$(0+2,0)=(2,0)$, $(1+2,1)=(3,1)$, $(4+2,2)=(6,2)$, $(9+2,3)=(11,3)$

Step5: Graph translated function

Connect the translated points with a smooth curve, defined for $x\geq2$.

Answer:

The graph of $g(x)=\sqrt{x-2}$ is the graph of $y=\sqrt{x}$ shifted 2 units to the right, passing through the points $(2,0)$, $(3,1)$, $(6,2)$, and $(11,3)$, with a domain of $x\geq2$.