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20 POINTS!!!
A polynomial function is shown below: f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function?

20 POINTS A polynomial function is shown below fx x3 3x2 4x 12 Which graph best represents the function class=
20 POINTS A polynomial function is shown below fx x3 3x2 4x 12 Which graph best represents the function class=

Respuesta :

altavistard
f(x) = x3 − 3x2 − 4x + 12    ( should be   f(x) = x^3 − 3x^2 − 4^x + 12 )

is a cubic function because its highest power of x is 3.  Because x^3 is positive, the graph starts in Quadrant III and ends in Quadrant I.  

The y-intercept is (0,12).

The greatest possible number of real roots is 3; the minimum number of real roots is 1.

Note that x=3 is a root of this function f(x) = x^3 − 3x^2 − 4^x + 12.  Thus, (3,0) is an x-intercept.  x=2 and x= -2 are also roots and lead to zero y-intercepts.

Can you now choose the correct graph?

If not, ask questions and I'll try to help you further. 
calculista

Answer:

the graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=x^{3}-3x^{2}-4x+12[/tex]    

Using a graphing tool

The x-intercepts of the function are the points [tex](-2,0),(2,0),(3,0)[/tex] (values of x when the value of the function is equal to zero)

The y-intercept of the function is the point  [tex](0,12)[/tex] (values of the function when the value of x is equal to zero)

the graph in the attached figure


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