Digital Agenda
Week of
October 26, 2015 to October 30, 2015
Unit 2: Functions
Check In/Do Now: Homework Corrections
Essential Question (s):
1. What is a function?
2. Can we use multiple representations of a function?
3. Can I name all the basic functions?
4. Can I find the domain and range of all functions?
Standard(s) from Instructional Guide:
PC.1.1.1 Determines the domain and range of functions as represented by symbols and graphs, where appropriate.
PC.1.2.3 Applies basic function transformations to a parent function f (x), including a • f (x), f (x) + d, f (x – c), f (b • x), |f (x)|, and f (|x|),
and interprets the results of these transformations verbally, graphically, and numerically.
PC.1.1.6 Compares and contrasts characteristics of different families of functions, such as polynomial, rational, radical, power,
exponential, logarithmic, trigonometric, and piecewise-defined functions, and translates among verbal, tabular, graphical, and symbolic
representations of functions.
PC.1.2.2 Forms the composition of two functions, and determines the domain, range, and graph of the composite function. Composes
two functions to determine whether they are inverses.
Student Objective (s): Students will:
2A I can explain the definition of a function, focusing on the relationship between the domain/input/pre-image and range/output/image. I can justify my
definition with examples and counterexamples (algebraic, graphic, mapping, and situations that illustrate a function relationship).
2B I can find the domain of a function. I can explain how restricted domain influences simplifying and solving radical, rational, and polynomial functions
(extraneous solutions).
2C I can find the domain of a linear inequality and a polynomial inequality (degree greater than or equal to 2) and explain the difference.
2D I can construct/deconstruct functions whose domain is another function. I can explain the connection to composite functions.
2E I can evaluate and simplify composite functions, including the difference quotient, using mathematical properties to justify the simplification.
2F I can illustrate a composite function graphically and connect domain and range to translations (shifting techniques) in piecewise functions, i.e.
f (x)  x 2 , f (x)  (x  2) 2  3. I can translate/shift the library of functions, including the greatest integer function.
2G I can use the definition of absolute value to graph as a piecewise function. I can explain how the definition connects to the piecewise function, i.e.
f (x)  x  4  2x  3
2H I can solve absolute value inequalities and equations and explain why the solution is valid.
2I I can determine whether a function is even, odd, or neither, and describe symmetry (about the origin versus about the y-axis).
Assessment and Student Reflection:
End of a lesson writing reflection and exit slips
.
WHOLE GROUP
Demonstrate how to use “ask myself “ questions to understand problems
1. What questions can you ask yourself to make sense of a problem?
2. What can you do if you get stuck on a problem?
3. Are there words that you don’t undersand?
4. What is the problem talking about?
5. What are the numbers/symbols in the problem and what do they mean?
DIRECT STATION
Lead a discussion in which students analyze
various functions.
Lead a group discussion in which students
Analyze the domain and range of various
functions
Lead a group discussion about graphing
Various functions
COLLABORATIVE STATION
Have students work on their own for
several minutes before interacting
with their partner. Partners should
focus on explaining to each other how
they arrived at the solution.
Students will review all functions
and its properties.
INDEPENDENT STATION
Review
www.ixl.com
1. Set Theory
2. Complex Numbers and
its subsets
3. Functions