# Functions

This topic covers: - Evaluating functions - Domain & range of functions - Graphical features of functions - Average rate of change of functions - Function combination and composition - Function transformations (shift, reflect, stretch) - Piecewise functions - Inverse functions - Two-variable functions

This course contains 30 segments:

**Evaluating functions**

Learn how to find the value of a function for a given input value.

**Inputs and outputs of a function**

Extend your understanding of the relationship between the inputs of a function and the outputs of that function.

**Functions and equations**

Understand the subtle differences and similarities between functions and equations. In this exercise, we will see how an equation can be turned into a function.

**Interpreting function notation**

Solve some word problems by interpreting expressions of modeling functions.

**Introduction to the domain and range of a function**

Learn what the domain and the range of a function are. Practice finding the domain and the range of a function given its graph.

**Determining the domain of a function**

Determine the domains of functions according to various considerations.

**Recognizing functions**

Learn how to distinguish between two-variable relationships that are functions and two-variable relationships that aren't functions.

**Piecewise functions**

Piecewise functions are functions that have different assignment rules for different numbers. For example, a function can return x² for any negative x-value and return x³ for any non-negative x-value.

**Maximum and minimum points**

Learn about maximum and minimum points of functions.

**Intervals where a function is positive, negative, increasing, or decreasing**

Learn about features of functions that have distinct graphical representations: intervals where the function is always positive or always negative, and intervals where the function is always increasing or always decreasing.

**Interpreting features of graphs**

Interpret the graphs of functions in terms of the contexts that are modeled by the functions.

**Average rate of change**

Learn what's the average rate of change of a function and how to find it over given intervals.

**Average rate of change word problems**

Solve word problems that concern the average rate of change of a functional relationship.

**Combining functions**

Learn how to take two basic functions and combine them into a new function which is their sum, difference, product, or quotient.

**Composing functions (Algebra 2 level)**

Learn what function composition is, how to to work with composite functions, and how to find the formulas of the composition of two functions.

**Shifting functions**

Learn how to transform functions so their graph is shifted horizontally or vertically. Learn how to find the equation of a function that is a shift of another function.

**Stretching functions**

Learn how to transform functions so their graph is stretched horizontally or vertically. Learn how to find the equation of a function that is a stretch of another function.

**Modeling situations by combining and composing functions (Algebra 2 level)**

Make use of knowledge in combining and composing functions, by modeling complex real-world situations.

**Introduction to inverses of functions (Algebra 2 level)**

Learn what inverses of functions are, and gain some experience with them by finding the outputs of the inverse of a function given that function.

**Finding inverse functions (Algebra 2 level)**

Learn how to find the inverses of polynomials functions, radical functions, and rational functions.

**Verifying that functions are inverses (Algebra 2 level)**

Learn how to check whether a pair of functions are the inverses of one another.

**Determining whether a function is invertible (Algebra 2 level)**

Learn about the conditions for a function to be invertible, and learn how to manipulate functions to make them invertible.

**Determining the domain of advanced functions (Algebra 2 level)**

Learn how to determine the domain of piecewise functions with different function rules.

**Determining the range of a function (Algebra 2 level)**

Learn how to find the range of a function, which is the set of all of the function's possible outputs.

**Graphing nonlinear piecewise functions (Algebra 2 level)**

Learn how to graph piecewise functions whose assignment rules are not linear.

**Interpreting the symmetry of algebraic models (Algebra 2 level)**

Learn how to interpret graphs of modeling functions in terms of their context by considering their symmetry.

**Interpreting the end behavior of algebraic models (Algebra 2 level)**

Learn how to interpret graphs of modeling functions in terms of their context by considering their end behavior.

**Interpreting the periodicity of algebraic models (Algebra 2 level)**

Learn how to interpret graphs of modeling functions in terms of their context by considering their periodicity.

**Comparing features of functions (Algebra 2 level)**

Learn how to compare various features between two functions, each represented in a different way.

**Two-variable functions**

Learn about functions that take *two* inputs in order to output a single value.

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Length | 30 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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Rating | Not enough ratings |
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Length | 30 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math Algebra |

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