Chapter 2.2, Problem 84E

(a)

To determine

To sketch: The graph of a polynomial function using leading coefficient test.

Explanation of Solution

Given information:

  $g(x)=x^4-4x^2$

Graph:

By leading coefficient test:

As the x⁴is a leading variable and its coefficient is 1 which is a positive coefficient

And x is having even number as its degree.

So when the large numbers were taken than x⁴ will be dominating

For $x<0$ negative large values are taken and the answer will be a positive number so the graph increases for $x<0$

For $x>0$ positive large values are taken and the answer will be a positive number so the graph increases for $x>0$

The graph will be

  

(b)

To determine

To Find: polynomial function using the real values of zeroes.

Answer to Problem 84E

The curve will pass through -2, 0 and 2.

Explanation of Solution

Given information:

  $g(x)=x^4-4x^2$

Graph:

The roots of the equation $g(x)=x^4-4x^2$

$\begin{array}{l}g(x)=x^4-4x^2\\ x^4-4x^2=0\\ x^2(x^2-4)=0\\ x^2(x+2)(x-2)=0\\ x=0\text{ , 2 ,-2}\end{array}$

The curve will pass through -2, 0 and 2.

(c)

To determine

To graph:Sketching the graph of a polynomial function

Explanation of Solution

Given information:

  $g(x)=x^4-4x^2$

Graph:

Plotting points:

  $g(x)=x^4-4x^2$

F(x)	x
-3	-1
0	0
-3	1

So the curve also passes through (-1,-3)(0,0)(1,-3)

  

(d)

To determine

To graph:Sketching the graph of a polynomial function.

Explanation of Solution

Given information:

  $g(x)=x^4-4x^2$

Graph:

Continuous curve through the points

Points are:(-2,0)(-1.414,-4)(-1,-3)(0,0)(1,-3)(1.414,-4)(2,0)