Answer:
The function has a double root
As x increases from negative infinity to positive infinity, the y-values increase, decrease and then increase
The domain and range of the function are the set of real numbers
Step-by-step explanation:
we have
[tex]f(x)=x^{3}-4x^{2}-3x+18[/tex]
using a graphing tool
see the attached figure
we know that
1) The y-intercept of the function f(x) (value of y when the value of x is equal to zero) is
For x=0
f(0)=18
so
The y-intercept is the point (0,18)
2) The roots of the function (or x-intercepts) are
x=-2 -----> with a multiplicity of 1
x=3 -----> with a multiplicity of 2
so
The x-intercepts are (-2,0) and (3,0)
3) As x increases from negative infinity to positive infinity, the y-values increase, decrease and then increase
4) As x approaches negative infinity , y approaches negative infinity
5) As x approaches positive infinity , y approaches positive infinity
6) The domain and range of the function are the set of real numbers
