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}

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 }

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct