Question

graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in section 1.2 and then applying the appropriate transformations.
$y = 7 + \sqrt{x + 5}$

Explanation:

Step1: Identify parent function

Parent function: $y=\sqrt{x}$

Step2: Apply horizontal shift

Shift left 5 units: $y=\sqrt{x+5}$

Step3: Apply vertical shift

Shift up 7 units: $y=7+\sqrt{x+5}$

Step4: Verify domain & shape

Domain: $x\geq-5$, graph starts at $(-5,7)$, increases slowly.

Answer:

The correct graph is the one with a starting point at $(-5,7)$, curving upward and to the right (the bottom-right option in the provided image, marked with the topmost radio button for that graph).