Question

Graph the function and identify all key characteristics f(x)=x^3-12x^2+45x-54

Answer 1

Answer:

We kindly ask you to see the explanation and the image attached below for further details.

Step-by-step explanation:

From Function Theory we know that third order polynomials are continuous functions with one relative minimum and one relative maximum and whose domain and range comprehends the set of all real numbers. Since the leading coefficient of the polynomial is positive, then two increasing intervals and only one increasing interval exist.

Now we proceed to graph the function and label each relevant information when possible.

Domain

$Dom \{f(x)\} = \mathbb{R}$

Range

$Ran \{f(x)\} = \mathbb{R}$

Zeros

x = 3 and x = 6