Question

which of these equations shifts a square root equation right 5 times and down once?
$y = \sqrt{x - 5} - 1$
$y = \sqrt{x - 5} + 1$
$y = \sqrt{x + 5} + 1$
$y = \sqrt{x + 5} - 1$

Explanation:

Step1: Recall transformation rules

For a square root function \( y = \sqrt{x} \), a horizontal shift right by \( h \) units is given by \( y=\sqrt{x - h} \), and a vertical shift down by \( k \) units is given by \( y=\sqrt{x}-k \).

Step2: Apply the shifts

We need to shift right 5 times, so \( h = 5 \), which gives \( \sqrt{x - 5} \). Then we shift down once, so \( k = 1 \), which gives \( y=\sqrt{x - 5}-1 \).

Answer:

\( y=\sqrt{x - 5}-1 \) (the first option: \( y = \sqrt{x - 5}-1 \))