Question

which of these equations shifts a radical equation right 1 time and up 2 times?
$y = \sqrt{x - 1} + 2$
$y = \sqrt{x - 2} + 1$
$y = \sqrt{x + 1} - 2$
$y = \sqrt{x + 2} - 1$

Explanation:

Step1: Recall horizontal shift rule

For a function \( y = f(x) \), a horizontal shift right by \( h \) units ( \( h>0 \)) is given by \( y = f(x - h) \). Here, we need a shift right by 1 unit, so for the radical function \( y=\sqrt{x} \), the horizontal shift gives \( y = \sqrt{x - 1} \).

Step2: Recall vertical shift rule

For a function \( y = f(x) \), a vertical shift up by \( k \) units ( \( k>0 \)) is given by \( y = f(x)+k \). Here, we need a shift up by 2 units, so we add 2 to the horizontally shifted function. So the function becomes \( y=\sqrt{x - 1}+2 \).

Answer:

\( y = \sqrt{x - 1}+2 \) (the first option, usually presented as the yellow - colored option in the given choices)