Which statement is true of the function f(x) = -∛X Check ALL that apply.The function is always increasing.The function has a domain of all real numbers.The function has a range of {y|– < y < }.The function is a reflection of y = .The function passes through the point (3, –27).

1) Given function: (x) = -∛x

2) Graph: see file attached which will help you to understand

3) Statements

- The function is always increasing. FALSE.

As x increase the value of the function decreases. For example for the positive values of x, as x grows - ∛x is becomes more negative.

- The function has a domain of all real numbers.TRUE

Cubic root  is defined for any real value of x which you can verify on the graph.

- The function has a range of {y|– < y < }.If it says - ∞ < y < ∞ it is TRUE

The range of the function is from - ∞ to + infinite. This is, it grows unlimitedly toward the two extremes.

- The function is a reflection of y = .If it says ∛x it is TRUE

Because multiplying by - 1 leads is the reflection over the x-axis

- The function passes through the point (3, –27). FALSE

f(3) = - ∛(3) which is not - 27.