Question

use transformations of ( f(x)=sqrt{x} ) to graph the following function. ( h(x)=sqrt{x - 3}+2 ) choose the correct graph below. a. graph a c. graph c b. graph b d. graph d

Explanation:

Step1: Identify parent function

Parent function: $f(x)=\sqrt{x}$, domain $x\geq0$, passes through $(0,0), (1,1), (4,2)$

Step2: Apply horizontal shift

For $h(x)=\sqrt{x-3}+2$, $x\to x-3$ shifts $f(x)$ right 3 units. New points: $(0+3,0)=(3,0)$, $(1+3,1)=(4,1)$, $(4+3,2)=(7,2)$

Step3: Apply vertical shift

Add 2 to output, shift up 2 units. Final points: $(3,0+2)=(3,2)$, $(4,1+2)=(4,3)$, $(7,2+2)=(7,4)$

Step4: Match to graph

The graph starts at $(3,2)$ and follows the square root curve shape, matching option C.

Answer:

C. (The graph starting at (3,2) and curving upward to the right)