Chapter 8.5, Problem 98E

(a)

To determine

The graph of the function $f\left(x\right)=\left(x^2-1\right)\left(x^2-4\right)$

Answer to Problem 98E

The Graph gets decreases and increases on both the axis.

Explanation of Solution

Given information:

Sketch the graph of each function as shown below,

  $f\left(x\right)=\left(x^2-1\right)\left(x^2-4\right)$

Formula used:

The function $f\left(x\right)=\left(x^2-1\right)\left(x^2-4\right)$ is equated to zero

Calculation:

Factor the completely as:

  $f\left(x\right)=\left(x+1\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

From the function, the zeros are: $-2,-1,1,2$

Plot the corresponding points: $\left(-2,0\right),\left(-1,0\right),\left(1,0\right),\left(0,0\right)$

To help determine the shape of the graph, find points between the zeros & plot them. Draw a smooth curve through the points:

  

Conclusion:

The Graph gets decreases and increases on both the axis.

(b)

To determine

The graph of the function $g\left(x\right)=x\left(x^2-1\right)\left(x^2-4\right)$

Answer to Problem 98E

The Graph gets decreases and increases on both the axis.

Explanation of Solution

Given information:

Sketch the graph of each function as shown below,

  $g\left(x\right)=x\left(x^2-1\right)\left(x^2-4\right)$

Formula used:

The function $g\left(x\right)=x\left(x^2-1\right)\left(x^2-4\right)$ is equated to zero

Calculation:

Factor the completely as:

  $g\left(x\right)=x\left(x+1\right)\left(x-1\right)\left(x+2\right)\left(x-2\right)$

From the function, the zeros are: $-2,-1,0,1,2$

Plot the corresponding points: $\left(-2,0\right),\left(-1,0\right),\left(0,0\right),\left(1,0\right),\left(0,0\right)$

To help determine the shape of the graph, find points between the zeros & plot them. Draw a smooth curve through the points:

  

Conclusion:

The Graph gets decreases and increases on both the axis.