Unit 8 More Functions, More Features
Lesson 1
Learning Focus
Relate the graph of a function to a story context.
Write a function made up of several functions.
Lesson Summary
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.
Lesson 2
Learning Focus
Graph piecewise functions.
Interpret piecewise functions.
Lesson Summary
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.
Lesson 3
Learning Focus
Relate piecewise functions to absolute value.
Identify features of an absolute value function.
Lesson Summary
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.
Lesson 4
Learning Focus
Use transformations to graph absolute value functions.
Write the equation that corresponds to the graph of an absolute value function.
Lesson Summary
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.
Lesson 5
Learning Focus
Model a context using two different ways of thinking about the variables.
Lesson Summary
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.
Lesson 6
Learning Focus
Find the inverse of a function given any representation.
Lesson Summary
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.
Lesson 7
Learning Focus
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.
Lesson Summary
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.
Lesson 8
Learning Focus
Add and subtract polynomials algebraically.
Add and subtract polynomials graphically.
Lesson Summary
In this lesson, we learned to add and subtract polynomials. We learned that the procedure used for adding and subtracting is analogous to adding whole numbers because polynomials have the same structure as whole numbers. Polynomials are added by adding like terms. When subtracting polynomials, we can avoid sign errors by adding the opposite of each term.
Lesson 9
Learning Focus
Multiply polynomials.
Raise binomials to powers.
Lesson Summary
In this lesson, we built on our understanding of area models from Algebra 1 to multiply polynomials. We learned to use either the box method or to distribute each term of the first factor to each term of the second factor. Both methods are based on the Distributive Property. We also learned an efficient method for raising binomials to powers using Pascal’s Triangle to help find the coefficient of each term in the expansion.
Lesson 10
Learning Focus
Support or challenge claims about different types of numbers and the result of adding, subtracting, multiplying, and dividing.
Support or challenge claims about the result of adding, subtracting, multiplying, and dividing polynomials.
Lesson Summary
In this lesson, we examined claims about the closure of sets of numbers and classes of functions under the operations of addition, subtraction, multiplication, and division. An example of such a claim is: The set of whole numbers is closed under division. A counterexample that shows this claim to be false is: