Question

Draw a machine diagram for the function. $$f(x)=\frac{3}{x-2}$$

   Draw a machine diagram for the function.
$$f(x)=\frac{3}{x-2}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 16

Instant Answer

Solved by Expert Sanchit Jain

09/29/2023

Step 1

First, we need to subtract 2 from the input x. So, the first machine will be "subtract 2". Show more…

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Draw a machine diagram for the function. $$f(x)=\frac{3}{x-2}$$

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Key Concepts

Function Machine Diagram

A function machine diagram is a visual tool used to represent the process by which an input is transformed into an output through a series of sequential operations. Each step in the diagram corresponds to a mathematical operation or function, showing how the initial input is modified until the final result is achieved.

Rational Function

A rational function is defined as the quotient of two polynomials. It is important because its form implies potential restrictions in the domain where the denominator cannot equal zero, and it often exhibits characteristics such as vertical asymptotes and discontinuities in its graph.

Domain Restrictions

Domain restrictions are the set of allowed input values for a function, specifically excluding any values that would make the function undefined, such as causing a division by zero. Recognizing these restrictions is crucial in the analysis and application of functions.

Function Transformations

Function transformations refer to the modifications applied to an input variable or function that result in shifts, stretches, compressions, or reflections of its graph. These operations help in understanding how the basic structure of a function is altered through various arithmetic or algebraic changes.

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