graph the cube root function and analyze the minimum and maximum on the given interval.\nf(x) = \\sqrt3{x +…

Explanation:

Step1: Analyze the function properties

The function $y = \sqrt[3]{x + 4}$ is a cube - root function. The parent function of $y=\sqrt[3]{x}$ is a one - to - one function that passes through the origin $(0,0)$ and has a domain and range of all real numbers. The function $y=\sqrt[3]{x + 4}$ is a horizontal shift of the parent function $y=\sqrt[3]{x}$ to the left by 4 units.

Step2: Evaluate the function at the endpoints of the interval

When $x=-7$, $y=\sqrt[3]{-7 + 4}=\sqrt[3]{-3}\approx - 1.44$. When $x = 9$, $y=\sqrt[3]{9+4}=\sqrt[3]{13}\approx2.35$.

Step3: Determine the behavior of the cube - root function

The cube - root function $y=\sqrt[3]{x}$ is increasing over its entire domain $(-\infty,\infty)$. So, $y=\sqrt[3]{x + 4}$ is also increasing over its entire domain.

Step4: Analyze the graphs

Since the function $y=\sqrt[3]{x + 4}$ is increasing on the interval $[-7,9]$, and $y(-7)\approx - 1.44$ and $y(9)\approx2.35$. We can eliminate graphs that do not show an increasing trend on the interval $[-7,9]$.

Answer:

(Without seeing the actual details of the graphs, we can't give a specific letter - choice. But the correct graph should be an increasing curve with the $y$ - value at $x=-7$ being approximately $-1.44$ and at $x = 9$ being approximately $2.35$)