Which statements correctly describe the graph of the function f(x) = x3 – 4x2 – 3x + 18? check all that apply.
there are three unique solutions to the function when y = 0.
the function has a double root.
as x increases from negative infinity to positive infinity, the y-values increase, decrease, and then increase again.
as x approaches negative infinity, y also approaches negative infinity.
the domain and range of the function are the set of real numbers.

The statements that apply are:


The function has a double root.

you can conclude that if you factor the polynomial as (x - 3)2 (x + 2), because x = 3 is a double root and x = - 2 is a single root.

As x increases from negative infinity to positive infinity, the y-values increase, decrease, and then increase again.

You can see that if you sketch the graph, y increases from netativity infinity until x = -1/3 (intermediate between the two different roots), then y starts to decrease until x = 3 (the value of the double root), and then y starts to increase again.

The domain and range of the function are the set of real numbers: there are not restrictions for the domain and y is not limited.