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Questions and Answers
What is the general form of a rational function?
What is the value of $[-4.5]$ using the integer value function?
What is the value of $f(4)$ for the piecewise function defined as $f(x)= \begin{cases} 2x - 4, & \text{if } x < 3 \ x^{2} + 1, & \text{if } 3 \le x < 7 \ 4, & \text{if } x \ge 7 \end{cases}$?
Which of the following values corresponds to $f(3)$ in the given piecewise function?
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What is the output of the integer value function for $ rac{5}{2}$?
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Study Notes
Rational Functions
- A rational function can be represented as the division of two polynomial functions P(x) and Q(x).
- The general form of a rational function is $f(x) = \frac{P(x)}{Q(x)}$, where Q(x) cannot be equal to zero.
Integer Value Function
- The integer value function, denoted by $f(x) = [x]$, maps a real number x to the greatest integer less than or equal to x.
- The function can be expressed as $f : R \rightarrow Z$ where $x \rightarrow [x]$.
Function Values
- The integer value of 4.1 is 4.
- The integer value of -4/3 is -2.
- The integer value of $\pi$ is 3.
- The integer value of -$\pi$ is -4.
Graphs of Functions
- A function can be defined differently for different intervals of x.
- Examples of function values are:
- f(2) = 0
- f(3) = 10
- f(4) = 17
- f(7) = 4
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Description
This quiz covers the essential concepts of rational and integer value functions. It explores the definitions, forms, and examples of these mathematical functions, including how they handle various inputs. Test your understanding of these functions through problems and examples provided.
