As x approaches infinity, which functions f(x) also approach infinity? How can : (x)=−0.7(2x−3)(−3x−5)        Be the correct answer when.... For functions with an even degree and a positive leading coefficient, the function will approach infinity as x approaches infinity. For functions with an odd degree and a positive leading coefficient, the functions will fall to the left and rise to the right, showing that it is approaching infinity as x is also. I thought that the LC HAD to be positive in order for the function to approach infinity? Please answer with understandable details  thanks alot

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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As x approaches infinity, which functions f(x) also approach infinity?

How can :

(x)=−0.7(2x−3)(−3x−5)

       Be the correct answer when....

For functions with an even degree and a positive leading coefficient, the function will approach infinity as x approaches infinity. For functions with an odd degree and a positive leading coefficient, the functions will fall to the left and rise to the right, showing that it is approaching infinity as x is also.

I thought that the LC HAD to be positive in order for the function to approach infinity?

Please answer with understandable details 

thanks alot

Expert Solution
Step 1

It's easy to see that the function that you have quoted is 

f(x)=-0.7(2x-3)(-3x-5)=(-1.4x+2.1)(-3x-5)=4.2x2+0.7x-10.5

So, the function does have positive leading coefficient.

Thus, limxf(x)=.

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