Key Concepts & Glossary
Key Equations
Rational Function |
Key Concepts
- We can use arrow notation to describe local behavior and end behavior of the toolkit functions and .
- A function that levels off at a horizontal value has a horizontal asymptote. A function can have more than one vertical asymptote.
- Application problems involving rates and concentrations often involve rational functions.
- The domain of a rational function includes all real numbers except those that cause the denominator to equal zero.
- The vertical asymptotes of a rational function will occur where the denominator of the function is equal to zero and the numerator is not zero.
- A removable discontinuity might occur in the graph of a rational function if an input causes both numerator and denominator to be zero.
- A rational function’s end behavior will mirror that of the ratio of the leading terms of the numerator and denominator functions.
- Graph rational functions by finding the intercepts, behavior at the intercepts and asymptotes, and end behavior.
- If a rational function has x-intercepts at , vertical asymptotes at , and no , then the function can be written in the form
Glossary
- arrow notation
- a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value
- horizontal asymptote
- a horizontal line y = b where the graph approaches the line as the inputs increase or decrease without bound.
- rational function
- a function that can be written as the ratio of two polynomials
- removable discontinuity
- a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function
- vertical asymptote
- a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a