# Domain of Rational Function

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 21, 2021.

1. ### nycmathguy

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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?

Last edited: Sep 21, 2021
nycmathguy, Sep 21, 2021

2. ### MathLover1

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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 MathLover1, Sep 21, 2021
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3. ### nycmathguy

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

2. What's wrong with my thread?

nycmathguy, Sep 21, 2021
4. ### nycmathguy

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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.

nycmathguy, Sep 21, 2021
5. ### MathLover1

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

MathLover1, Sep 21, 2021
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