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.
