Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]
The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]
Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex]
[tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex]
[tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex]
[tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]
The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
