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Pre-Calculas
| Term | Definition |
|---|---|
| Function Notation | a relation in which ever input results in one and only one output; usually denoted with f(X), g(X), h(X), k(X) and other letters. |
| Radical function | f(X)=square root of x |
| Radicand | the value under the square root |
| Rational function | f(X)=1/x |
| Domain (inputs) | all possible inputs (x-values) of a function. independent values in the equation |
| Denominator Restriction | domain values that render a rational expression undefined |
| Square root (even root) Restriction | domain values that render a square root expression undefined |
| Range (outputs) | all possible outcomes (y- values) of a function; values that are dependent in an equation of an expression |
| Interval notation | a way to indicate inequalities by using brackets or parenthesis instead of inequality symbols. |
| U(union) | symbol used to merge two or more pieces of an interval |
| Point of discontinuity | an x- value on the graph where the y is undefined |
| continuous graph | a graph with a domain of (- infinity, + infinity) |
| Dissentious graph | a graph with a domain OTHER than (- infinity, + infinity) |
| Vertical Asymptote | domain values that render a rational expression undefined. |
| Horizontal Asymptote | range values that render a rational expression undefined |
| Vertical shrink/stretch | occurs when a function is multiplied by a constant, a. If a is between 0 and 1, there is a vertical shrink (or compression). if a is greater than 1, there is a vertical stretch. Both by a factor of a. |
| Horizontal shrink/stretch | occurs when a functions output is multiplied by a constant b. If b is between o and 1, there is a horizontal stretch by a factor of 1/b if b is greater than 1, there is a horizontal shrink (or compression) by a factor of 1/b |
| Horizontal translation left/right | occurs when a constant is added to or subtracted from a function input. adding a constant = translation right. |
| Vertical translation up/down | occurs when a constant is added to or subtracted from a function. adding = translation up subtracting =translation down. |
| Reflection across x-axis | occurs when a function is (X) by (-) coefficient |
| Rigid Transformation | a transformation that does NOT alter the size or shape of a function |
| Nonrigid Transformation | a transformation that does alter the size or shape of a graph (e.g dictation) |
| Piecewise function | a function made up of multi sub-equations, where each sub function applies to a different interval in the domain |
| Evaluate | finding the output value of a function f(x) that corresponds to a given input value, x |
| Vertical line test | a visual method used to determine whether a given curve is a function or not |
| Increasing interval | an interval in which the y-value increases |
| Decreasing interval | an interval in which the y-value decreases as the x-value increases |
| Boundedness | the limits or bounds of a function |
| a) boundedness above | a function is bounded above by the #A is the #A is higher than or equal to all values of the function |
| b) boundedness below | a function is bounded below by the #B if #B is lower than or equal to all values of the function |
| c) bounded | a function that is bounded below and above |
| d) unbounded | a function that is neither bounded below of above |
| bounded on an interval | an interval is bounded when both its endpoints are included in the domain. |
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