Polynomial functions are expressions with variables raised to non-negative integer powers, like $f(x) = 3x^2 - 2x + 1$. Rational functions are fractions where the numerator and denominator are polynomials, such as $g(x) = \frac{x+2}{x-1}$. This worksheet will help you practice key concepts and vocabulary related to these functions.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Polynomial | A. A function that can be written as a ratio of two polynomials. |
| 2. Rational Function | B. The highest power of the variable in a polynomial. |
| 3. Degree | C. A value that makes the denominator of a rational function equal to zero. |
| 4. Vertical Asymptote | D. An expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents. |
| 5. Leading Coefficient | E. The coefficient of the term with the highest degree in a polynomial. |
Complete the following paragraph:
A polynomial function is an expression with __________ raised to non-negative integer __________. A rational function is a __________ where the numerator and __________ are polynomials. A __________ asymptote occurs where the denominator of a rational function equals zero.
Explain, in your own words, the key differences between polynomial and rational functions. Give an example of each.
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