Chapter 1.8, Problem 21HP

To determine

To describe: the end behavior of the graph.

Explanation of Solution

The end conduct of a capacity f portrays the conduct of the diagram of the capacity at the finishes of the $x$ -axis.

At the end of the day, the end conduct of a capacity depicts the pattern of the chart on the off chance that we look to the correct finish of the $x$ -axis (as  $x$  approaches $+\infty$ ) and to one side finish of the $x$ -axis.

  

For example, consider this graph of the polynomial function f. Notice that as you move to the right on the  $x$ -axis, the graph of f goes up. This means, as $x$  gets larger and larger,  $f\left(x\right)$ , get larger and larger as well.

Mathematically, we write: as $x\to \infty ,f(x)\to \infty .$ (Say, as $x$  approaches positive infinity,  $f\left(x\right)$ , approaches positive infinity.)

  

On the opposite finish of the graph, as we move to one side along the $x$ -axis (imagine $x$  approaching $-\infty$ ), the diagram of f goes down. This implies as $x$ gets increasingly negative, $f\left(x\right)$ , likewise gets increasingly negative.

Mathematically, as $x\to -\infty ,f(x)\to -\infty .$ (Say, as  $x$  approaches negative infinity).