Chapter 6.4, Problem 2CYU

To determine

To graph: the function by making table of domain x and range y.

Answer to Problem 2CYU

The graph is a curve which is shown here in red color curve.

Explanation of Solution

Given:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^{\text{4}}{\text{+4x}}^{\text{3}}{\text{+2x}}^{\text{2}}\text{+x-3}$ .

Concept used:

The graph of the function $\text{f}$ is the set of all point in the plane of the form $\left(\text{x,f}\left(\text{x}\right)\right)$ .

The graph can be define by the graph of $\text{f}$ and the equation for the graph will be $\text{y=f}\left(\text{x}\right)$ .

The graph of the function is special case of the graph of an equation.

Calculation:

The function is given as:

  $\text{f}\left(\text{x}\right){\text{=-2x}}^{\text{4}}{\text{+4x}}^{\text{3}}{\text{+2x}}^{\text{2}}\text{+x-3}$ .

The table for the graph of the function will be:

By putting the value $\text{x}$ the value of $\text{y}$ can be determine.

$\text{x}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$	$\text{3}$	$\text{2}\text{.395}$	$\text{1}\text{.814}$
$\text{f}\left(\text{x}\right)$	$-8$	$-3$	$\text{0}$	$7$	$\text{-36}$	$\text{0}$	$7.616$

The points in the graph so collected will form a graph for the given equation.

The leading coefficient is positive and an even degree polynomial. The graph intersects in the x-axis at $\text{2}$ points, indicating there are two zeroes for the function.

The graph of the given equation by collecting the points will be:

  

Hence the graph is a curve which is shown here in red color curve.