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.

Question

Carson Olson

Mathematics

14 December, 18:53

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.

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Answers (1)

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Christopher Jacobs · Answer 1

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.