Question

Analyze each polynomial function$f.$

$f\left(x\right)=x^3-2.91x^2-7.668x-3.8151$

Short answer

The given function is:

$f\left(x\right)=x^3-2.91x^2-7.668x-3.8151$

Step-by-step solution

Given Information

The given function is:

$f\left(x\right)=x^3-2.91x^2-7.668x-3.8151$

The polynomial function

$f\left(x\right)=x^3+2.91x^2-7.668x-3.8151$

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

The $y$-intercept is $f\left(0\right)=-3.8151$ and x-intercepts are $-0.9$ and$4.71.$

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

$x$	$y$
$-1$	$-0.06$
$0$	$-3.82$
$4$	$-17.05$
$5$	$10.09$

The function has $2$turning points: $(-0.9,0)$and $(2.84,-26.16).$

Domain: $x\in \mathrm{ℝ}$Range: all real numbers

Function is increasing on the intervals $(-\infty ,-0.9)$and $(2.84,\infty )$and decreasing on the interval $(-0.9,2.84).$

The graph