Across
- 5. A function assigns each input exactly one output. It is a fundamental concept in mathematics that describes the relationship between variables.
- 6. The domain of a function includes all the possible input values (x-values) for which the function is defined. It often excludes values that result in division by zero or undefined expressions.
- 8. A vertical line runs parallel to the y-axis. Vertical asymptotes are common in rational functions and show where the function's value approaches infinity.
- 11. Simplification is the process of reducing an expression to its simplest form. This is a common step when working with rational functions or algebraic expressions.
- 13. A horizontal line runs parallel to the x-axis. Horizontal asymptotes describe the end behavior of a function as x approaches infinity or negative infinity.
- 14. To factor means to express a number or polynomial as a product of its divisors or factors. This is often used in simplifying rational expressions or partial fraction decomposition.
- 15. A piecewise function is defined by different expressions over different intervals of its domain. These functions are often used to model situations with distinct phases or conditions.
- 16. Disjoint intervals are intervals that do not overlap. In piecewise functions, disjoint intervals define separate parts of the domain where different expressions apply.
- 19. An asymptote is a line that a graph approaches but never intersects. Vertical and horizontal asymptotes help describe the behavior of rational functions at extreme values.
Down
- 1. The behavior of a function refers to how its values change as the input changes. Asymptotes and limits describe the end behavior of rational functions.
- 2. A polynomial is an expression consisting of terms that are powers of a variable with constant coefficients. Rational functions are often expressed as the ratio of two polynomials.
- 3. An interval is a range of values along the x-axis for which a function is defined. Intervals are commonly written in interval notation, using parentheses and brackets.
- 4. A constant is a value that does not change. In step functions, the value of the function remains constant within each interval.
- 7. A limit describes the behavior of a function as its input approaches a specific value. Limits are used to understand the function's behavior at points of discontinuity or infinity.
- 9. Extraneous solutions are values that emerge during the process of solving an equation but do not satisfy the original equation. They often arise in rational equations when terms are canceled incorrectly.
- 10. A discontinuity occurs when a function is not continuous at a specific point. This can be caused by holes, jumps, or vertical asymptotes in the graph.
- 12. The x-intercept is where the graph of a function crosses the x-axis, and the y-intercept is where it crosses the y-axis. These points are essential for graphing functions.
- 16. Decomposition is the process of breaking a rational function into simpler fractions. This technique is known as partial fraction decomposition and is used in integration and simplification.
- 17. A rational function is a ratio of two polynomials. It is defined for all real numbers except where the denominator is zero.
- 18. The range of a function consists of all possible output values (y-values) that result from plugging in values from the domain. It is determined by the behavior of the function's graph.