Question

describe the transformation of the graph of the parent function $y = \sqrt{x}$ for the function $y = \sqrt{x + 7} + 5$. the graph is shifted 7 units \\(\boldsymbol{\downarrow}\\) and 5 units \\(\boldsymbol{\downarrow}\\).

Explanation:

Step1: Analyze horizontal shift

For a function \( y = \sqrt{x + h} \), if \( h>0 \), the graph shifts \( h \) units left. Here, \( y=\sqrt{x + 7} \) (comparing to \( y = \sqrt{x} \)), so \( h = 7>0 \), shift 7 units left.

Step2: Analyze vertical shift

For a function \( y=\sqrt{x}+k \), if \( k > 0 \), the graph shifts \( k \) units up. Here, \( y=\sqrt{x + 7}+5 \), so \( k = 5>0 \), shift 5 units up.

Answer:

The graph is shifted 7 units left and 5 units up.