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What is the range of the function r(x) = 1/(1 - x)^2? Express your answer in interval notation.

Question:

What is the range of the function {eq}r(x) = \frac{1}{(1 - x)^2} {/eq}? Express your answer in interval notation.

Range of a Rational Function:

The domain and range of any function can be found by graphical or analytical methods. In the case of rational functions, the range can be found by analytical methods where the horizontal asymptote is used to establish how this would be.

Answer and Explanation:

Function:

{eq}r\left(x\right)=\frac{1}{\left(1-x\right)^2} {/eq}


Range:

To find the range of a function, you can choose two methods, the graphical method and the analytical method. The analytical method consists of first finding the horizontal asymptote of the function and from there the range is established.


Since the function we have is one where the degree of the denominator is greater than the degree of the denominator, the horizontal asymptote will be a constant function {eq}y=0 {/eq}.


The range will be: {eq}\:\left(0,\:\infty \:\right) {/eq}


Learn more about this topic:

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Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
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