consider the graph of equation y=lx^3-8l?

Question

Find the domain D for the function y=f(x). And Please write answer in interval notation.

Answer 1

y = x^3 - 81
if y = 0 . . . . . x = 4.3267 . . (4.3267 ,0)
if x = 0 . . . y = - 81 . . . (0, - 81)

x^3 = y+ 81 . . . differentiating
3 x^2 x ' = 1
x ' = 1/ 3 x^2 . . . . it has no vertical tangent

domain in y has no limit

Answer 2

It looks like the function is y = ABS(x^3 - 8), where ABS means absolute value. Then the domain is (- inf,inf).