Chapter 6.4, Problem 58STP

(a)

To determine

To find:theend behaviour of the graph.

Answer to Problem 58STP

  $\begin{array}{l}x\to \infty ;f\left(x\right)\to \infty .\\ x\to -\infty ;f\left(x\right)\to -\infty .\end{array}$

Explanation of Solution

Given:

  

Concept used:

For an even degree function the end behaviour will be same direction.

For an odd degree function the end behaviour will be in different direction.

If $a>0$ .

Then curve will be open ward.

Or

The end point of the curve will be:

up and up for even.

Down and up for odd.

If $a<0$ .

Then curve will be down ward.

The end point of the curve will be:

Down and down for even.

Up and down for odd.

Calculation:

The curve equation is

  $y=a{x}^2+bx+c$ .

If $a>0$ .

Then curve will be open ward.

There will be one extreme value from the graph show the point will be Minimum.

As

  $\begin{array}{l}x\to \infty .\\ f\left(x\right)\to \infty .\\ x\to -\infty .\\ f\left(x\right)\to -\infty .\end{array}$

Hence, $\begin{array}{l}x\to \infty ;f\left(x\right)\to \infty .\\ x\to -\infty ;f\left(x\right)\to -\infty .\end{array}$

(b)

To determine

To find:whether the graph represent even degree or an odd degree function.

Answer to Problem 58STP

The graph will be even degree.

Explanation of Solution

Given:

  

Concept used:

If number of cut in the x-axis or zeroes in the axis is even then the function is even degree function.

and if number of cut in the x-axis or zeroes in the axis is odd then the function is odd degree function.

Calculation:

According to the given:

Since the graph cut the x-axis at two points so the graph will be even degree.

Hence, the graph will be even degree.

(c)

To determine

To find:The number of real zeroes in the graph.

Answer to Problem 58STP

There is $2$ zeroes.

Explanation of Solution

Given:

  

Concept used:

The number of real zeroes is the number of intersections with x-axis by the curve or number cut made by the curve on x-axis.

Calculation:

Zeroes can be calculated as the number of cut in the x-axis by curve.

Since there is $2$ cut in the x-axis by the curve.

Therefore, there will be $2$ zeroes.

Hence, there is $2$ zeroes.