Domain of Rational Function

Section 2.6
Question 6



f(x) = 5x/(x + 2)

The denominator is zero when x = -2.

x + 2 = 0

x = -2

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

To discuss the behavior of f near any excluded values of x, it is best to evaluate a few values to the left and right of x = -2.

x-values left of 0

Let x = -4

f(-4) = 5(-4)/(-4 + 2)

f(-4) = -20/-2

f(-4) = 10

Let x = -3

f(-3) = 5(-3)/(-3 + 2)

f(-3) = 15

x-values right of 0

Let x = 2

f(2) = 5(2)/(2 + 2)

f(2) = 10/4

f(2) = 2.5

Let x = 1

f(1) = 5(1)/(1 + 2)

f(1) = 5/3

f(1) = 1.66

As x nears -2 from the left side, the graph shoots upward to positive infinity.

As x nears -2 from the right side, the graph shoots download to negative infinity.

Is my understanding correct here?

P. S. Please, check out my thread from yesterday at 9:16pm: Find Zeros of Polynomial Function.

 

discuss the behavior of f near any excluded values of x=-2 only

all you need is:

Limit from the left


Limit from the right

 

1. This is a precalculus question. Why bring calculus into play?

2. What's wrong with my thread?

 

As x nears -2 from the left side, the graph shoots upward to positive infinity.

As x nears -2 from the right side, the graph shoots download to negative infinity.

Is this not the same as your limit reply?

 

yes, it's same as my limit reply just wanted to show you shorter way to do it

 

Thanks.