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Unit 1 Vocab
Lesson 1-9
| Term (Lesson 1) | Definition |
|---|---|
| Function Notation | a relation in which every input results in one and 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 Functions | 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 symbols |
| 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 |
| 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 multiplied by a negative coefficient |
| Reflection across 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 Function | 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 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 intervale |
| 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 Tes | 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) |
| 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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