graph the function. give the minimum and maximum values over the specified interval. f(x)=√(x + 8), 4≤x≤9 a…

Explanation:

Step1: Analyze the function's behavior

The function $f(x)=\sqrt{x + 8}$ is a square - root function. The square - root function $y=\sqrt{u}$ is an increasing function when $u\geq0$. Here $u=x + 8$, and for $4\leq x\leq9$, as $x$ increases, $f(x)$ increases.

Step2: Find the minimum value

Substitute the lower - bound of the interval $x = 4$ into the function $f(x)$. $f(4)=\sqrt{4 + 8}=\sqrt{12}=2\sqrt{3}$

Step3: Find the maximum value

Substitute the upper - bound of the interval $x = 9$ into the function $f(x)$. $f(9)=\sqrt{9+8}=\sqrt{17}$

Answer:

The minimum value is $2\sqrt{3}$