Answer:
Shown below
Step-by-step explanation:
To solve this problem, we need to analyze the leading coefficient and the roots of the polynomial function:
[tex]f(x)=x^3-6x^2+11x-6[/tex]
Recall that a polynomial function can be represented by:
[tex]f(x)=a_{n}(x)+ \ldots +a_{1}x+a_{0}[/tex]
So the leading coefficient is [tex]a_{n}[/tex]. In our problem, this coefficient is [tex]a_{n}=1[/tex]
Since [tex]n[/tex] is odd and the leading coefficient [tex]a_{n}>0[/tex], then the graph must falls to the left and rise to the right. Also, the roots are [tex]x_{1}=1 \ x_{2}=2 \ and \ x_{3}=3[/tex]. So the only graph that matches this is the fourth one as indicated below.
