Question

the graph of the parent function is shown. identify which function would represent shifting the parent function 1 unit down and 5 units right
options:
y = sqrt3{x + 5} - 1
y = sqrt3{x - 5} - 1
y = sqrt{x + 5} - 1
y = sqrt{x - 5} - 1

Explanation:

Step1: Identify parent function

The graph matches $y=\sqrt{x}$, the square root parent function.

Step2: Apply horizontal shift rule

Shifting right 5 units replaces $x$ with $x-5$, giving $y=\sqrt{x-5}$.

Step3: Apply vertical shift rule

Shifting down 1 unit subtracts 1 from the function, giving $y=\sqrt{x-5}-1$.

Step4: Match to options

Compare the transformed function to the given choices.

Answer:

D. $y = \sqrt{x-5}-1$