PC FIP – Unit 1
Unit 1 Learning Target: Graph, Analyze, and Transform Functions.
Identify required previous knowledge to promote student success:
1) Classify functions by specific operations in the equation.
2) Recognize general graphic shapes by function classification.
3) Graph a function using transformation represented in equation.
4) Evaluate a function: f(a) = b.
5) Substitute an algebra expression in to a function: f(x – a).
6) Identify Domain and Range of a function using an equation or graph.
7) Use point-slope form equation to write an equation of a line.
Review-Preview Assignments:
Writing the Domain for Functions
Evaluating and Substituting Functions
Graphing and Analyzing Functions
Writing Linear Equations with Point-Slope Form
Formative Assessments:
Pretest
Exit Tickets
Review Preview Quiz
Unit 1a Learning Target: Identify, graph, and analyze piecewise, greatest integer,
and absolute value functions.
Knowledge Target(s):
1) Recognize the graph and equation of an absolute value, piecewise and greatest
integer functions.
2) Evaluate an Absolute Value, Piecewise and Greatest-Integer functions.
Reasoning Target(s):
1) Algebra operations in a function’s equation will transform a function’s graph.
2) Absolute Value, Piecewise and Greatest-Integer functions all have points of
discontinuity because of the operations that exist in the equations.
3) An Absolute Value function can be represented as a Piecewise function.
4) The Greatest-Integer function only yields integers.
5) To preserve the definition of a function, the point of discontinuity belongs to one
part of the graph or one part of an equation for a Piecewise or Greatest-Integer
function.
Procedure Skills Target(s):
1) Identify, graph, and analyze Absolute Value, Piecewise and Greatest-Integer
functions.
2) Write an Absolute Value function as a Piecewise function.
Product Target(s):
1) Apply problem-solving skills to the solution of real-world problems.
2) Use the mathematic language to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly.
3) Demonstrate the appropriate role of technology.
Scaffolding:
Initially, students take a pretest to assess previous and existing skill level. In
addition, students will be given review/preview worksheets to improve
previous skills to prepare to learn new skills. Students will work in cooperative
learning groups based on skill level.
After reviewing how to graph, evaluate, and analyze a relation, students will
begin with graphing and analyzing simple Absolute Value Functions. Next,
students will write the same absolute value functions as a Piecewise Functions.
Then, students will graph and analyze Piecewise and Greatest-integer Functions
Assignment: Absolute Value and Kuta Software Worksheets
Formative Assessment(s): Exit Ticket and Quiz
Modifications:
Technology: Instructional videos on Teacher Webpage and use of graphing
calculators to graph functions or see symmetry(s).
Unit 1b Learning Target: Transform functions graphically and algebraically,
including graphing and writing its inverse.
Knowledge Target(s):
1) Recognize the notation for an inverse function is 𝑓(𝑥).
2) Identify a transformation: reflection, stretch/compression, or translation.
3) Understand that a function’s inverse reverses what the original function did.
Reasoning Target(s):
1) Any algebraic operation will transform every ordered-pair (x, y) on a function’s
graph.
2) The inverse function reverses the original input (x) and output (y) values:
If 𝑓(𝑎) = 𝑏, then 𝑓 −1 (𝑏) = 𝑎.
3) A reflection over the line y = x switches the x- and y-values for every orderedpair.
4) The graph of an inverse function is a reflection of the original function over the
line y = x.
5) Any many-to-one function’s domain must be restricted to find its inverse
equation and/or graph.
Procedure Skills Target(s):
1) Write the equation of any algebraic transformation and graph any
transformation.
2) Write the equation for and graph a function’s inverse.
Product Target(s):
1) Apply problem-solving skills to the solution of real-world problems.
2) Use the mathematic language to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly.
3) Demonstrate the appropriate role of technology.
Scaffolding:
Initially, students take a pretest to assess previous and existing skill level. In
addition, students will be given review/preview worksheets to improve
previous skills to prepare to learn new skills. Students will work in cooperative
learning groups based on skill level.
Students will begin finding the inverse of a function by reflecting the order-pairs
that satisfy the function over the line y = x by switching the x- with the y-value.
Next, students will continue practicing the same skill with many-to-one
functions by restricting the domain. Then students will write algebraic equations
for inverse functions by switching the x- with the y-variable and solving for the yvariable and restricting the domain when necessary.
Assignment: Worksheets
Formative Assessment(s):
Modifications:
Technology: Instructional videos on Teacher Webpage and use of graphing
calculators to graph functions or see symmetry(s).
Unit 1c Learning Target: Use an algebraic test to determine if a relation has
symmetry.
Knowledge Target(s):
1) Identify and visualize any symmetry with the x-axis, y-axis, origin, or line y = x.
2) Know and apply algebraic tests for the x-axis, y-axis, origin, or line y = x.
Reasoning Target(s):
1) Any symmetry implies that there is a relationship within or between the x- and
y-values.
2) The relationship that exists within or between the x- and y-values holds
algebraically.
Procedure Skills Target(s):
1) Determine if and algebraically verify a relation has symmetry.
Product Target(s):
1) Apply problem-solving skills to the solution of real-world problems.
2) Use the mathematic language to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly.
3) Demonstrate the appropriate role of technology.
Scaffolding:
Initially, students take a pretest to assess previous and existing skill level. In
addition, students will be given review/preview worksheets to improve
previous skills to prepare to learn new skills. Students will work in cooperative
learning groups based on skill level.
Students will begin by reflecting ordered-pairs over specific lines to observe
relationships within and between the x- and y-values. Then students will identify
graphs with symmetries. Finally students will check for and verify a relation’s
symmetry algebraically.
Assignment: Worksheets
Formative Assessment(s):
Modifications:
Technology: Instructional videos on Teacher Webpage and use of graphing
calculators to graph functions or see symmetry(s).
Unit 1d Learning Target: Classify functions as even, odd, or neither.
Knowledge Target(s):
1) Identify functions as even, odd, or neither based on symmetry or algebraic
equations.
Reasoning Target(s):
1) Exponential values of a polynomial will determine if the function is even, odd, or
neither.
Procedure Skills Target(s):
1) Classify functions as even, odd, or neither
Product Target(s):
1) Apply problem-solving skills to the solution of real-world problems.
2) Use the mathematic language to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly.
3) Demonstrate the appropriate role of technology.
Scaffolding:
Initially, students take a pretest to assess previous and existing skill level. In
addition, students will be given review/preview worksheets to improve
previous skills to prepare to learn new skills. Students will work in cooperative
learning groups based on skill level.
Students will investigate symmetry in polynomials with all even exponents, all
odd exponents, and a combination of both to identify symmetries. Next, students
will check and verify symmetries algebraically. Then, students will continue
practicing this skill with radical and rational functions.
Assignment: Worksheets
Formative Assessment(s):
Modifications:
Technology: Instructional videos on Teacher Webpage and use of graphing
calculators to graph functions or see symmetry(s).
Unit 1e Learning Target: Graph and Analyze Radical functions
Knowledge Target(s):
1) Identify the shape of a radical function depending on the root value.
Reasoning Target(s):
1) The domain and range of a radical function with an even root value is limited
because of the values of the radicand must be positive.
2) Output values of radical functions change very slowly because of the root.
3) Every radical function with an odd root value and without a vertical and
horizontal shift will pass through the origin.
Procedure Skills Target(s):
1) Graph and analyze radical functions.
Product Target(s):
1) Apply problem-solving skills to the solution of real-world problems.
2) Use the mathematic language to communicate increasingly complex ideas orally
and in writing, using symbols and notations correctly.
3) Demonstrate the appropriate role of technology.
Scaffolding:
Initially, students take a pretest to assess previous and existing skill level. In
addition, students will be given review/preview worksheets to improve
previous skills to prepare to learn new skills. Students will work in cooperative
learning groups based on skill level.
Students will begin graphing and analyzing radical functions with square roots
by using a table with perfect squares as a radicand and recognizing and
visualizing transformations. Then, students will continue the same practice with
cubic roots. Finally, students will continue the same practice with 4th- and 5throots.
Assignment: Worksheets
Formative Assessment(s):
Modifications:
Technology: Instructional videos on Teacher Webpage and use of graphing
calculators to graph functions or see symmetry(s).