Question

Analyze each polynomial function f.

$f\left(x\right)=x^3+2.56x^2-3.31x+0.89$

Short answer

The given functions is:

$f\left(x\right)=x^3+2.56x^2-3.31x+0.89$

Step-by-step solution

Given Information

The given functions is:

$f\left(x\right)=x^3+2.56x^2-3.31x+0.89$

The polynomial function

$f\left(x\right)=x^3+2.56x^2-3.31x-0.89$

The polynomial function $f$is of degree 3 and the graph behaves like $y=x^3.$

The $y$-intercept is $f\left(0\right)=0.89$ and $x$-intercepts are $3.56$ and$0.5.$

Values of x on each side of the x-intercepts:

$x$	$y$
$-4$	$-8.91$
$-3$	$6.86$
$0$	$0.89$
$1$	$1.14$

• The function has 2 turning points: $(-2.21,9.92)$and $(0.5,0).$
• Domain: $x\in \mathrm{ℝ}$Range: all real numbers
• The function is increasing on the intervals $(-\infty ,-2.21)$ and $(0.5,\infty )$ and decreasing on the interval$(-2.21,0.5).$
  

The graph