Question

If $f(x)=\frac{x}{x-3},$ find $f(-2), f(0),$ and $f(3)$

   If $f(x)=\frac{x}{x-3},$ find $f(-2), f(0),$ and $f(3)$

Precalculus: Functions and Graphs

Precalculus: Functions and Graphs

Earl W. Swokowski,… 11th Edition

Chapter 2, Problem 4

Instant Answer

Solved by Expert Babita Kumari

10/27/2020

Step 1

So, we get $f(-2)=\frac{-2}{-2-3}$. Show more…

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If $f(x)=\frac{x}{x-3},$ find $f(-2), f(0),$ and $f(3)$

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Key Concepts

Rational Functions

Rational functions are functions that are expressed as the ratio of two polynomials. They are characterized by having potential restrictions in their domains because the denominator may become zero. Analyzing rational functions often involves understanding asymptotic behavior, discontinuities, and the impact of undefined values on the function's graph.

Domain of a Function

The domain of a function is the set of all possible input values for which the function is defined. For rational functions, this means identifying values that do not cause division by zero. Understanding the domain is crucial for avoiding undefined expressions and for a correct interpretation of the function's behavior.

Function Evaluation

Function evaluation is the process of determining the output of a function for a given input. This involves substituting the input value into the function's formula and simplifying the result. It is a fundamental concept that underlies much of algebra and calculus, as it allows us to understand the behavior of functions at specific points.

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