Question

Analyze each polynomial function.

$f\left(x\right)=2x^4-\pi x^3+\sqrt{5}x-4$

Short answer

The Given function is:$f\left(x\right)=2x^4-\pi x^3+\sqrt{5}x-4$

Step-by-step solution

Given Information

The Given function is:$f\left(x\right)=2x^4-\pi x^3+\sqrt{5}x-4$

The polynomial function

$f\left(x\right)=2x^4-\pi x^3+\sqrt{5}x-4$

The polynomial function $f$is of degree $4$and the graph behaves like $y=2x^4.$

The $y$-intercept is $f\left(0\right)=-4$and $x$-intercepts are $-1.07$and $1.62.$

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

$x$	$y$
$-2$	$48.66$
$-1$	$-1.09$
$1$	$-2.91$
$2$	$7.34$

The function has $1$turning point: $(-0.42,-4.64).$

Domain:$x\in \mathrm{ℝ}$Range: $<-4.64,\infty >$

The function is increasing on the intervals $(-0.42,\infty )$and decreasing on the interval role="math" localid="1648570864975" $(-\infty ,0.42).$

The graph