Chapter 15.1, Problem 55E

To determine

To find:

The end behavior of the given function.

Explanation of Solution

Given:

The function

  $y=4x^5-2x+4$

Concept used:

The left hand limit and right hand limit of a function $f$ at a point $x=a$ are , equal

  $\begin{array}{l}\underset{x\to a^{-}}{\lim }f\left(x\right)=L\\ \underset{x\to a^{+}}{\lim }f\left(x\right)=L\end{array}$

Calculation:

The function

  $y=4x^5-2x+4$

Degree is odd $=5$

Leading coefficient is $+5$

End behavior :

Down in $3rd$ quadrant and up in $1st$ quadrant

As

  $\begin{array}{l}x\to -\infty ,y\to -\infty \\ \text{and}\\ x\to \infty ,y\to \infty \end{array}$

Draw the graph

  $y=4x^5-2x+4$