Function Faceoff Slides Function Faceoff
Algebra 2 STAAR Blueprint
WICOR Strategy: Focused Note-Taking & Collaboration
ID: STAAR-2026
LVL: ADVANCED
The Mission
Identify & Analyze
Master key attributes of Quadratic, Exponential, Logarithmic, and Rational functions.
Transformations
Predict how changing parameters affects the graph's physical behavior.
Collaborative Inquiry
Use AVID strategies to solve complex STAAR-level problems together.
WICOR Checklist
Writing: Building your Field Guide
Inquiry: Analyzing function patterns
Collaboration: Team Showdown
Organization: Focused Note-Taking
Reading: Interpreting word problems
Phase 1: Quadratic Recall
Parent Function: \(f(x) = x^2\)
SECT_01
Vertex Form: \(f(x) = a(x - h)^2 + k\)
\(a\): Width & Direction (Reflection)
\((h, k)\): Vertex (Turning Point)
Critical Features
Axis of Symmetry \(x = h\)
Range (if \(a > 0\)) \(y \ge k\)
Zeros Quadratic Formula
U-SHAPE: PARABOLA
Phase 2: Growth & Decay
Inverse Operations: \(y = b^x\) vs \(y = \log_b(x)\)
SECT_02
Exponential
Asymptote: Horizontal (\(y = k\))
Domain: All Real Numbers
Key Form: \(y = a \cdot b^{(x-h)} + k\)
Logarithmic
Asymptote: Vertical (\(x = h\))
Range: All Real Numbers
Key Form: \(y = a \log_b(x-h) + k\)
"Logs are just exponents flipped over the line \(y = x\)"
Phase 3: Rational Breakdowns
Parent Function: \(f(x) = \frac{1}{x}\)
SECT_03
Vertical Asymptote
Set the denominator to zero and solve.
Horizontal Asymptote
Compare degrees: High/Low, Same/Same, or Low/High.
Holes
Occur when factors cancel out from numerator and denominator.
Visualizing Discontinuity
Collaborative Showdown
Now, transition to your teams. You have 20 minutes to complete the Showdown Worksheet using your Field Guide notes.
Rules of Engagement
Every team member must participate in the inquiry process.
Justify every answer with an attribute (asymptote, vertex, etc.).
Be ready to present your "Blueprint" solution to the class.
Closing & Reflection
Take 3 minutes to summarize your learning in the Summary section of your Focused Notes.
Final Inquiry Question:
"How does identifying the inverse of a function help you find its key attributes, specifically its domain, range, and asymptotes?"
STAAR Ready
Function Field Guide Notes WICOR
Function Field Guide
Algebra 2 STAAR Blueprint : Focused Notes
STUDENT REGISTRY
Name:
Date:
Essential Question
How can I identify and predict the physical behavior and key attributes of different parent functions based on their algebraic transformations?
Keywords & Cues
Vertex Form
Transformations: h, k, a
Asymptotes
Vertical vs Horizontal
Inverses
Domain/Range swap
Holes vs. V.A.
Rational Discontinuity
Instructional Notes & Examples
Phase 1: Quadratics
Focus: \(f(x) = a(x - h)^2 + k\)
Phase 2: Exp & Log
Relationship: \(b^y = x \iff \log_b(x) = y\)
Phase 3: Rationals
Focus: Discontinuity, Asymptotes, and Holes
Summary & Reflection
Write a 3-5 sentence summary of the relationships between the attributes of parent functions and their transformations. How does this help you on the STAAR test?
Function Showdown Worksheet Showdown Worksheet
Collaborative Inquiry Blueprint
Team ID:
Agents:
Work with your team to analyze each function "blueprint." Justify your choice by identifying specific key attributes (vertex, asymptotes, holes, etc.). Accuracy and reasoning are required for victory.
Case 01: Quadratic Shift
STAAR 2.A4.B
Function \(g(x)\) is a transformation of the parent function \(f(x) = x^2\). The graph of \(g(x)\) is shifted 3 units left and 5 units down, then vertically stretched by a factor of 2.
Task:
Identify the vertex and the range of \(g(x)\). Write the equation in vertex form.
Blueprint Analysis (Show Work)
Vertex
Equation
Case 02: Growth Boundary
STAAR 2.A5.B
Consider the function \(h(x) = 3(0.5)^{(x+2)} - 4\).
Task:
Determine if this is growth or decay. Identify the horizontal asymptote and the y-intercept.
Blueprint Analysis (Show Work)
Type
Asymptote
y-intercept
Case 03: Logarithmic Limit
STAAR 2.A5.E
The graph of \(f(x) = \log_2(x-4) + 1\) is shown in a technical drawing. A student claims the vertical asymptote is at \(x = 1\).
Inquiry Challenge:
Evaluate the claim. Identify the correct vertical asymptote and the domain of the function.
Blueprint Analysis (Evidence)
Verdict (True/False & Correct V.A.)
Domain Statement
Case 04: Rational Discontinuity
STAAR 2.A6.K
Analyze the rational function: \[R(x) = \frac{2x^2 - 8}{x^2 - 4x + 4}\]
Critical Analysis:
Determine the vertical asymptote(s), horizontal asymptote, and any holes in the graph.
Calculations & Factoring Area
Vert. Asymptote
Horiz. Asymptote
Holes (at x=)
Collaborative Debrief
Summarize your team's strategy for identifying attributes quickly during the STAAR test:
Function Faceoff Teacher Guide Teacher Facilitation Guide
Function Faceoff : STAAR Mastery
AVID WICOR Strategy
Lesson Flow & Pacing
00-10m
Opening & Hook:
Introduce the "Blueprint" theme. Students set up their Function Field Guide (Focused Notes).
10-40m
Focused Instruction (The Slides):
Direct instruction on the 3 phases. Students use the right-hand column for sketches and rules, and the left column for "Cues" (Inquiry).
40-75m
Collaborative Showdown (The Worksheet):
Teams of 3-4 tackle the Blueprint Cases. Encourage "Inquiry-based talk"—students must justify answers with attributes.
75-90m
Reflection & Exit Ticket:
Students complete the Cornell Summary and the individual Exit Ticket.
WICOR Elements
W Notes & SummaryI Analyzing blueprintsC Team ShowdownO Cornell Note StructureR Interpreting math text
Answer Key: Showdown Worksheet
Case 01: Quadratic
Vertex: \((-3, -5)\)Range: \(y \ge -5\)Equation: \(g(x) = 2(x + 3)^2 - 5\)
Case 02: Exponential
Type: Decay (\(b = 0.5\))Asymptote: \(y = -4\) (Horizontal)y-intercept: \((0, -3.25)\) (Solve \(3(0.5)^2 - 4\))
Case 03: Logarithmic
Verdict: False. The V.A. is at \(x = 4\) (set argument to 0).Domain: \(x > 4\)
Case 04: Rational
Simplified: \(R(x) = \frac{2(x+2)(x-2)}{(x-2)^2} = \frac{2(x+2)}{x-2}\)Vert. Asymptote: \(x = 2\)Horiz. Asymptote: \(y = 2\) (Same degree)Holes: None (Factors do not fully cancel, the zero at \(x=2\) is still in denominator). Note: If denominator was \((x-2)(x+3)\), hole would be at \(x=2\).
Scaffolding & Differentiation
For Struggling Learners:
Provide a "Transformation Cheat Sheet" that explicitly defines \(h\), \(k\), and \(a\) for each function type.
Final Blueprint Exit Ticket Final Blueprint
Mastery Check : Individual Assessment
Name:
Date:
Inquiry Question 01
A rational function \(f(x)\) has a vertical asymptote at \(x = -3\) and a horizontal asymptote at \(y = 1\). Which of the following could be the equation for \(f(x)\)?
\(f(x) = \frac{x-3}{x+1}\)
\(f(x) = \frac{x+1}{x+3}\)
\(f(x) = \frac{3x}{x-1}\)
\(f(x) = \frac{x+3}{x-1}\)
Inquiry Question 02
Describe the transformation of \(g(x) = \log_4(x + 5) - 2\) from its parent function \(f(x) = \log_4(x)\). Specifically, identify the vertical asymptote and the domain .
Justification & Attributes
Vert. Asymptote
Domain
Inquiry Question 03
Given the quadratic function \(q(x) = -2(x - 4)^2 + 8\), what is the maximum value of the function and what is the range?
Security Clearance: STAAR READY
Ref: UNIT-FUNC-001
