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 base function

Base function: $y=\sqrt{x}$ (domain $x\geq0$, range $y\geq0$)

Step2: Apply horizontal shift

Shift $y=\sqrt{x}$ left 5 units: $y=\sqrt{x+5}$ (domain $x\geq-5$)

Step3: Apply vertical shift

Shift $y=\sqrt{x+5}$ up 7 units: $y=7+\sqrt{x+5}$ (range $y\geq7$)

Step4: Match to graph

The graph has domain $x\geq-5$, range $y\geq7$, matching the middle lower graph.

Answer:

The correct graph is the middle lower option (the one with x-axis extending to 10, y-axis starting at -2, and the curve beginning at $(-5,7)$ and increasing rightward).