Find each function value. See Example 9 . The total revenue...

Find each function value. See Example $9 .$ The total revenue from the sale of a popular book is approximated by the rational function $R(x)=\frac{1000 x^{2}}{x^{2}+4},$ where $x$ is the number of years since publication and $R(x)$ is the total revenue in millions of dollars. A. Find the total revenue at the end of the first year. B. Find the total revenue at the end of the second year. C. Find the revenue during the second year only. D. Find the domain of function $R$

Find each function value. See Example $9 .$
The total revenue from the sale of a popular book is approximated by the rational function $R(x)=\frac{1000 x^{2}}{x^{2}+4},$ where $x$ is the number of years since publication and $R(x)$ is the total revenue in millions of dollars.
A. Find the total revenue at the end of the first year.
B. Find the total revenue at the end of the second year.
C. Find the revenue during the second year only.
D. Find the domain of function $R$

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Key Concepts

Incremental Change Calculation

Calculating the difference between function values at two points is a method used to determine the incremental change over an interval. This concept is particularly useful in determining the change within a specific period, such as finding the revenue generated during a particular year.

Domain of a Function

The domain of a function is the set of all possible input values for which the function is defined. In the context of rational functions, this typically means identifying and excluding values that cause the denominator to be zero, as these lead to undefined expressions.

Rational Functions

Rational functions are expressions formed by dividing one polynomial by another. They are widely used to model various real-world situations, such as revenue, where the behavior of the function can vary dramatically depending on the degree and coefficients of the numerator and denominator.

Function Evaluation

Function evaluation involves substituting a specific value into a function to calculate the corresponding output. This concept is fundamental in determining the exact value of the function at a given point, which is crucial for applications like calculating cumulative totals at specific time intervals.

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