Question

the function y =³√-x – 3 is graphed only over the domain of {x | –8 < x < 8}. what is the range of the graph? a). {y | –5 < y < 5} b). {y | –5 < y < –1} c). {y | 1 < y < 5} d). {y | 1 < y < –1}

Answer 1

$y=\sqrt[3]{-x}-3\ and\ x\in(-8;\ 8)\\\\subtitute\ x=-8\ and\ x=8\ to\ the\ equation:\\\\y=\sqrt[3]{-(-8)}-3=\sqrt[3]8-3=2-3=-1\\\\y=\sqrt[3]{-8}-3=-2-3=-5\\\\Answer:\boxed{\{y|-5 \ \textless \ y \ \textless \ -1\}}\to\fbox{b.}$

Answer 2

Answer:

correct option is b) {y  : -5 < x < - 1 }

Step-by-step explanation:

The graph of function y = ∛-x -3 over the domain of {x : -8 < x < 8 } is shown in figure-1

Range is set of Y values for which the function is define.

So, in order to find the range , we need to find the corresponding y values for given domain.

Put x = -8 in  y = ∛-x -3 then we get,

                 y = ∛-x -3

                 y = ∛-(-8) -3

                 y = ∛8 -3

                 y = 2 -3

                  y = - 1

Put x = 8 in  y = ∛-x -3 then we get,

                 y = ∛-(8) -3

                 y = ∛-8 -3

                 y = -2 -3

                  y = - 5

Hence the range of function y = ∛-x -3 over the domain of {x : -8 < x < 8 } is

{y  : -5 < x < - 1 }

correct option is b) {y  : -5 < x < - 1 }