Unit 1 Functions and Their Inverses
Model a relationship between two quantities by using either quantity as the input variable.
In this lesson, we explored two different ways of viewing a relationship between two quantities. We examined how changing the input quantity changes the output quantity and the relationship between the two functions that are formed using story context, tables, graphs, and equations. We identified features of linear inverse functions that can be seen in each of the representations.
Understand the inverse of a quadratic function.
Determine the relationship between the domain and range of a function and its inverse.
Understand when the inverse of a function is also a function.
In this lesson, we examined a quadratic function and its inverse. We found characteristics of inverse functions that are common across function types. We learned that some functions are invertible and that if a function is not invertible, the domain can be restricted to make it invertible.
Represent the inverse of an exponential function.
Compare the inverse relationship for an exponential function with the inverses of linear and quadratic functions.
Determine if a function is invertible.
In this lesson, we modeled the inverse of an exponential function to determine its features. We learned that this type of function is called a logarithmic function, which we will learn more about in Unit 2. We also discussed a way to describe the input-output relationship of inverse functions using mathematical notation.
Understand the input-output relationship between a function and its inverse.
Find the inverse of a function.
In this lesson, we learned that the equation of the inverse function has the inverse operations in the reverse order of the original function. Using this idea, we learned a method for finding the inverse of a function if the function is invertible or the domain has been restricted to make it invertible.
Match a function and its inverse given a table, a graph, or an equation.
Use a representation of a function to create a second representation.
In this lesson, we matched a function and its inverse with different representations. We found strategic ways to see if the inputs and outputs of the two functions have been switched. We also learned to verify that two functions are inverses using