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Math
Oklahoma Math
Precalculus (PC): Functions (F)
Interpret characteristics of a function defined by an expression in the context of the situation.
Sketch the graph of a function that models a relationship between two quantities, identifying key features.
Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.
Describe end behavior, asymptotic behavior, and points of discontinuity.
- Classify discontinuities
- Continuity at a point
- Continuity at a point (algebraic)
- Continuity at a point (graphical)
- Continuity over an interval
- Discontinuities of rational functions
- End behavior of algebraic models
- End behavior of algebraic models
- End behavior of polynomials
- End behavior of polynomials
- End behavior of rational functions
- Functions continuous at specific x-values
- Functions continuous on all real numbers
- Graphing rational functions according to asymptotes
- Graphs of polynomials
- Graphs of polynomials: Challenge problems
- Graphs of rational functions
- Graphs of rational functions: horizontal asymptote
- Graphs of rational functions: vertical asymptotes
- Graphs of rational functions: y-intercept
- Graphs of rational functions: zeros
- Infinite limits and asymptotes
- Intro to end behavior of polynomials
- Rational functions: zeros, asymptotes, and undefined points
- Removable discontinuities
- Removing discontinuities (factoring)
- Removing discontinuities (rationalization)
- Types of discontinuities
- Worked example: Continuity at a point (graphical)
Determine if a function has an inverse. Algebraically and graphically find the inverse or define any restrictions on the domain that meet the requirement for invertibility, and find the inverse on the restricted domain.
Model relationships through composition, and attend to the restrictions of the domain.
Rewrite a function as a composition of functions.
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Interpret the meanings of quantities involving functions and their inverses.
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Verify by analytical methods that one function is the inverse of another.
- Composite and inverse functions: FAQ
- Determine if a function is invertible
- Determining if a function is invertible
- Intro to invertible functions
- Using specific values to test for inverses
- Verify inverse functions
- Verifying inverse functions by composition
- Verifying inverse functions by composition
- Verifying inverse functions by composition: not inverse
- Verifying inverse functions from tables
Predict solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
Graphically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
Algebraically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.
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