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You need to find the domain and the range of the function y = -3 root(3)(x+4).

Since every real number has a cube root that is unique, hence any real value of x works such that the domain of the function y = -3 root(3)(x+4) is the real set R.

Since the domain is R, hence the range of this function is also R.

Sketching the graph of the function yields:

You may find the points this curve passing plugging x real values in y = -3root(3)(4+4)

Hence, if x = 4 => y = -3root(3)(8) => y = -6

If x = -12=> y=-3root(3)(-12+4) = -3root(3)(-8) = 6

You may verify the values above on the curve such that: You need to pick x=4 on x axis and you need to rise from x=4 a orthogonal line that intersect the curve at a point. You need to draw an orthogonal projection to y axis and you will see that they will intersect at y = -6.

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