Question

Analyze each polynomial function.

$f\left(x\right)=-1.2x^4+0.5x^2-\sqrt{3}x+2$

Short answer

The given function is

$f\left(x\right)=-1.2x^4+0.5x^2-\sqrt{3}x+2$

Step-by-step solution

Step 1. Given Information

The given function is

$f\left(x\right)=-1.2x^4+0.5x^2-\sqrt{3}x+2$

The polynomial function

$f\left(x\right)=-1.2x^4+0.5x^2-\sqrt{3}x+2$

The polynomial function $f$is of degree $4$and the graph behaves like $y=-1.2x^4$.

The $\mathrm{y}-\mathrm{intercept}$is$f\left(0\right)=2$i.e. $\left(0,2\right)$

And the is where $x-\mathrm{intercept}$where $f\left(x\right)=0$i.e.$\left(-1.47,0\right)\mathrm{and}\left(0.913,0\right)$

Step 3. Analysis from the graph

The value of the given function around$x-\mathrm{intercept}$is as follow:

$x$	$y$
$-1.5$	$-0.352$
$1$	$-0.432$

There is one turning point i.e. $\left(-0,809,0.3214\right)$

Domain: $x\in \mathrm{ℝ}$, Range:$y\in [3.21,\infty )$

The function is increasing in the interval role="math" localid="1652327307581" $(-\infty ,-0.809]$and decreasing int he interval$[-0.809,\infty )$

Step 4. The graph