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Pre calculus
UE1
| Term | Definition |
|---|---|
| Function Notation | Relation every input results in one and only output. Ex: f(x) |
| Radical Function | F(x) = /x |
| Radicand | Value under square root |
| Rational Function | F(x) = 1/x |
| Domain | X-value of possible inputs |
| Denominator Restriction | Domain values that render rational expression undefined |
| Square root Restriction | Domain values that render square root expression undefined |
| Range | All possible outcomes (y-Value) of function |
| Interval Notation | Indicate inequalities by using brackets or parenthesis instead of inequality symbols |
| U Union | Symbol used to verge 2 or more pieces of an interval |
| Point Of Discontinuity | An x-value on graph where y-value is undefined |
| Continuous Graph | A graph with a domain of (-00,00) |
| Discontinuous Graph | A graph with a domain other than (-00,00) |
| Vertical stretch/shrink | Occurs when function x by constant, a if a between 0 and 1 is vertical stretch, both by factor of a |
| Horizontal stretch /shrink | Occurs when function inputs x by a constant, b if b is between 0 and 1 ->>>>Horizontal stretch by a faction 1/b. If b is greater than 1 = Horizontal shrink or compression) by factor 1/b |
| Horizontal translation left/right | Occurs a constant is + or - from a function input + a constant + left, - a constant + right |
| Vertical asymptote | Domain value render rational expression undefined |
| Horizontal asymptote | Range value render rational expression undefined |
| Vertical trans. Up/down | Occurs a constant is + to i or - from function. += up: - =n down (translation) |
| Reflection across x-axis | Occurs a functions is x by a - coefficient |
| Reflection across y-axis | Occurs a functions input is x by a - coefficient |
| Rigid transformation | Does not alter the size or shape of function |
| Non rigid transformation | Does alter the size or shape of a graph |
| Piecewise function | Function made up of multiple sub-equations, where sub-function applies to diff. Interval domain |
| Evaluate | Find output value of f(x) that corresponds to a given input value x |
| Vertical line test | Visual method to determine a given curve is a function or not |
| Increasing | An interval in y-value going up as the x value is up |
| Decreasing | An interval in y value is going down as the x value is going up |
| Boundedness | Limits or bounds of function |
| Bounded above | Function is bounded above by the number of B if number B is higher than or equal to all values of function |
| Bounded below | Function is bounded below by the number of B if number B is lower than or equal to all values of function |
| Bounded | Function that is bounded both above and below |
| Unbounded | A function that is neither bounded above nor below |
| Bounded on an interval | An interval is bounded both its endpoints plus included in domain |
| Extrema | Point which is max or min value - of function is obtained in some interval |
| Local (relative) | Point is a max or min relative to points around it |
| Absolute | Highest or lowest point in entire domain |
| Maximum | Largest y-value of a function over a set domain/increasing to decreasing |
| Minimum | Smallest y-value of function over a set of a domain/decrease to increase |
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