Domain of Rational Function...2

[nycmathguy]

Section 2.6
Question 8

f(x) = (2x)/(x^2 - 4)

Set x^2 - 4 to zero and solve for x.

x^2 - 4 = 0

x^2 = 4

sqrt{x^2} = sqrt{4}

x = -2, x = 2.

Domain = ALL REAL NUMBERS except for x = -2 and x = 2.

I say the two x-values are the vertical asymptotes.

Discuss the behavior of f near the excluded values of x.

Limit of f(x) as x tends to -2 from the right side is positive infinity.

Limit of f(x) as x tends to 2 from the left side is negative infinity.

You say?

 

[MathLover1]

way to go!

 

[nycmathguy]

way to go!

Thank you.

Can you take a look at the link below?

https://www.math-forums.com/threads/find-zeros-of-polynomial-function.441296/