Which statements correctly describe the graph of the function f(x) = x3 – 4x2 – 3x + 18? Select three options. 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 approaches positive infinity. The domain and range of the function are the set of real numbers.

The function is:

f(x) = x^3 - 4*x^2 - 3*x + 18.

Below, you can see the graph of the function.

The statements that are true are:

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

You can see this in the graph and may be really hard to see it without the graph, the easier way would be to see the derivate of f(x) and see that is first positive, then negative, and then positive.

f'(x) = 3*x^2 - 8*x - 3

As the leading coefficient is positive, the arms oppen up, and f'(0) = -3

Then is easy to see that from left to right, is positive, then negative, and then positive again.

The domain and range of the function are the set of real numbers.

For the domain, we do not have any denominator nor weird function that has problems in a particular value, so the domain is the set of all real numbers.

And as you can see, as the leading coefficient is an odd power of x, the range will go from minus infinity to infinity (you can also see it in the graph).

The function has a double root.

Yes, in the graph you can see two roots, but this is a 3rd-degree polynomial, so it must have 3 roots, this means that one of the roots in the graph is a double root. (Where the double root is at x = 3, as you can see in the graph)