Unit 4 More Functions, More Features
Relate the graph of a function to a story context.
Write a function made up of several functions.
In this lesson, we learned about piecewise functions, functions that combine several pieces that each have their own equation into one function. We graphed and wrote equations for piecewise functions. We learned that the equations for each part of the function are called sub-functions, each with their own domain that tells what part of the piecewise function they define.
Graph piecewise functions.
Interpret piecewise functions.
In this lesson, we graphed piecewise functions and learned that some are discontinuous. We learned how to indicate on a graph whether the point was included in an interval. We also made connections between point-slope form for a line and vertex form for a quadratic function.
Relate piecewise functions to absolute value.
Identify features of an absolute value function.
In this lesson, we learned about the linear absolute value function. We learned that absolute value functions can be written as piecewise functions or using the operation because they have two distinct parts. We identified the domain and range and graphed the function.
Use transformations to graph absolute value functions.
Write the equation that corresponds to the graph of an absolute value function.
In this lesson, we learned the quick-graph method for graphing absolute value functions using transformations. We learned to change from absolute value to piecewise form and to identify the vertex and line of symmetry from either form.
Model a context using two different ways of thinking about the variables.
In this lesson, we learned about inverse functions using a context that had two different and useful ways to think of the relationship. Two functions are called inverse functions when their inputs and outputs have been switched.
Find the inverse of a function given any representation.
In this lesson, we learned that the equation of an inverse function will contain the inverse operations in the reverse order. We used this idea to find a procedure to solve for the equation of the inverse of a function.
Write and graph piecewise functions efficiently and accurately.
Write and graph absolute value functions in piecewise and absolute value form.
Find inverses and graph inverse functions efficiently and accurately.
In this lesson, we worked on becoming more fluent with piecewise functions, absolute value functions, and inverse functions. We learned to be more efficient in our work and to refine the details so that it is entirely correct.