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Unit 1 Vocab Pre Cal
| Term | Definition |
|---|---|
| LESSON 1: Function Notation | a relation in which every 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)= √x |
| Radicand | the value under the square root |
| Rational Function | f(x)= 1/x |
| Domain (inputs) | all possible inputs (x-values) of a function; values that are independent in an equation or expression |
| 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 or expression |
| Interval Notation | A way to indicate inequalities by using brackets or parenthesis instead of inequality system. |
| U (union) | Symbol used to merge 2 or more pieces of an interval |
| Point of Discontinuity | an x-value on the graph where the y-value is undefined |
| Continuous Graph | a graph with a domain of (-∞, ∞) |
| Discontinuous Graph | a graph with a domain OTHER THAN (-∞, ∞) |
| Vertical Asymptote | domain values that render a rational expression undefined |
| Horizontal Asymptote | range values that render a rational expression undefined |
| LESSON 2: Vertical Stretch/Shrink | 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 Stretch/Shrink | Occurs when a function's input is multiplied by a constant, b. If b is between 0 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's input. Adding a constant = translation left; Subtracting a constant = translation right. |
| Horizontal Translation Up/Down | occurs when a constant is added to or subtracted from a function. Adding = translation up; Subtracting = translation down. |
| Vertical Translation Up/Down | occurs when a constant is added to or subtracted from a function. Adding = translation up; Subtracting = translation down. |
| Reflection Over X-Axis | occurs when a function is multiplied by a negative coefficient. |
| Reflection Over Y-Axis | Occurs when a function's INPUT is multiplied by a negative coefficient. |
| LESSON 3: 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., dilation) |
| LESSON 4 AND 5: Piecewise Functions | a function made up of multiple 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 |
| LESSON 6: Increasing | an interval in which the y-value increases as the x-value increases. |
| Decreasing | an interval in which the y-value decreases as the x-value increases. |
| Boundedness | the limits or bounds of a function. |
| Bounded Above | a function is bounded above by the number A if the number A is higher than or equal to all values of the function |
| Bounded Below | a function is bounded below by the number B if the number B is lower than or equal to all values of the function |
| Bounded | a 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 when both its endpoints are included in the domain |
| Extrema | a point at which a maximum or minimum value of the function is obtained in some interval |
| Local(relative) | the point is a max or min relative to the points around it |
| Absolute | the highest or lowest point in the entire domain |
| Maximum | the largest y-value of a function over a set domain; the point where the function changes from increasing to decreasing |
| Minimum | the smallest y-value of a function over a set domain; the point where the function changes from decreasing to increasing |
| LESSON 8: Composition of Functions | a function made of other functions, where the output of one function is the input of another function (f∘g)(x)=f(g(x)): "f of g", indicates that g(x) is the input to f(x). |
| Not Commutative | the property that order DOES matter when composing |
| Restricted Domain | a domain for a function that is smaller than the function's domain of definition; typically used to specify a one-to-one section of a function |
| Decomposition | breaking a given composed equation into the inner and outer function |
| LESSON 9: Inverse Relation | a set of ordered pairs obtained by interchanging the first and second coordinates of each pair in the original function |
| Horizontal Line Test | a test consisting of drawing horizontal lines through a function to prove whether it is one-to-one and therefore has an inverse that is also a function. |
| One-to-One | any output value, y, in a function has exactly one input, x. If a function is one-to-one, then it has an inverse that is also a function. |
| Inverse Function | a function that undoes the action of another function. A function g is the inverse of a function f if y=f(x) then x=g(y). 5. f^(−1) (x):"f inverse" |
| Inverse Reflection Principle | a function and its inverse will be reflections of each other over the line y=x. |
| Inverse Composition Rule | when f and g are inverse, the composition of f and g (in either order) creates a function that for every input returns the input: f(g(x))=g(f(x))=x. *** When composing two inverse functions fand f^(−1), f(f^(−1) (x))=f^(−1) (f(x))=x. |
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