the function $y = sqrt3{-x}-3$ is graphed only over the domain of ${x|-8leq xleq8}$. what is the range of…

the function $y = sqrt3{-x}-3$ is graphed only over the domain of ${x|-8leq xleq8}$. what is the range of the graph?\n${y|-5leq yleq5}$\n${y|-5leq yleq - 1}$\n${y|1leq yleq5}$\n${y|1leq yleq - 1}$

the function $y = sqrt3{-x}-3$ is graphed only over the domain of ${x|-8leq xleq8}$. what is the range of the graph?\n${y|-5leq yleq5}$\n${y|-5leq yleq - 1}$\n${y|1leq yleq5}$\n${y|1leq yleq - 1}$

Answer

Explanation:

Step1: Analyze the function for extreme - value of domain

We have the function (y = \sqrt[3]{-x}-3) and the domain (-8\leq x\leq8). When (x=-8), substitute (x = - 8) into the function: [y=\sqrt[3]{-(-8)}-3=\sqrt[3]{8}-3=2 - 3=-1]

Step2: Analyze the function for other extreme - value of domain

When (x = 8), substitute (x = 8) into the function: [y=\sqrt[3]{-8}-3=-2 - 3=-5] Since the cube - root function (y=\sqrt[3]{-x}-3) is a continuous function over the domain ([-8,8]), the range of the function is ({y|-5\leq y\leq - 1}).

Answer:

({y|-5\leq y\leq - 1})