Investigate the behavior of the function as x grows large by making a table of function values and plotting a graph.2х + 1f(x)4х — 6What value does the function approach as x grows large?

Given function is fx=2x+14x−6 We have to find the end behavior of fx=2x+14x−6 Now,…

Answered: Investigate the behavior of the…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 60SE: The height h of a projectile is a function of the time t it is in die air. The height in feet for t...

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Investigate the behavior of the function as x grows large by making a table of function values and plotting a graph.
2х + 1
f(x)
4х — 6
What value does the function approach as x grows large?

Expert Solution

Step 1

Given function is $f (x) = \frac{2 x + 1}{4 x - 6}$

We have to find the end behavior of $f (x) = \frac{2 x + 1}{4 x - 6}$

Now,

$\begin{matrix} \lim_{x \to \infty} f (x) = \lim_{x \to \infty} (\frac{2 x + 1}{4 x - 6}) \\ = \lim_{x \to \infty} (\frac{x (2 + \frac{1}{x})}{x (4 - \frac{6}{x})}) \\ = \lim_{x \to \infty} \frac{(2 + \frac{1}{x})}{(4 - \frac{6}{x})} \\ = \frac{2}{4} \\ = \frac{1}{2} \end{matrix}$

Hence, $\lim_{x \to \infty} f (x) = \frac{1}{2}$

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