Question

Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits

Answer 1

Given:

`h(x)=(x-1)^3(x+3)^2`

The x-intercepts of the given polynomial are

`x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}`

Substitute x=0 in h(x) to find y-intercepts.

`\text{ y-intercepts =}(-1)^3(3)^2=-9`
`\lim _(x\to-\infty)h(x)=\lim _(x\to-\infty)(x-1)^3(x+3)^2=-\infty`

`as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty`

`\lim _(x\to\infty)h(x)=\lim _(x\to\infty)(x-1)^3(x+3)^2=\infty`

`as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty`

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.