Question

1. the graph of $y = -sqrt{x}$ is shifted 2 units up and 5 units left. which equation represents the new graph?

options:
$y = -sqrt{x + 5} + 2$
$y = -sqrt{x - 5} + 2$
$y = -sqrt{x + 2} - 5$
$y = -sqrt{x - 2} + 5$

Explanation:

Step1: Recall the transformation rules

For a function \( y = f(x) \), shifting it \( h \) units left/right and \( k \) units up/down gives \( y = f(x + h) + k \) (left: \( h>0 \), right: \( h<0 \); up: \( k>0 \), down: \( k<0 \)).

Step2: Apply the transformations to \( y = -\sqrt{x} \)

• Shift 5 units left: Replace \( x \) with \( x + 5 \), so we get \( y = -\sqrt{x + 5} \).
• Shift 2 units up: Add 2 to the function, so \( y = -\sqrt{x + 5} + 2 \).

Answer:

A. \( y = -\sqrt{x + 5} + 2 \)