Chapter 6.4, Problem 3CYU

To determine

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

Answer to Problem 3CYU

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

Explanation of Solution

Given:

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

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:

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

The table for the graph of the function will be:

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

$\text{x}$	$\text{-2}$	$\text{-1}$	$\text{0}$	$\text{1}$	$\text{2}$	$1.82$	$1.218$	$-0.392$
$\text{f}\left(\text{x}\right)$	$\text{66}$	$\text{0}$	$\text{-4}$	$-6$	$\text{6}$	$0$	$-6.374$	$\text{-4}\text{.388}$

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 green color curve.