Model Mashup Graphic Organizer Model Mashup
Graphic Organizer: Comparing Function Families
Name: __________________________
Date: ___________________________
Linear
Standard Form / Parent
\(f(x) = x\)
Rate of Change
Table Pattern
Key Visual Features
Quadratic
Standard Form / Parent
\(f(x) = x^2\)
Rate of Change
Table Pattern
Key Visual Features
Exponential
Standard Form / Parent
\(f(x) = b^x\)
Rate of Change
Table Pattern
Key Visual Features
Transformation Master Key: \(g(x) = a \cdot f(x - h) + k\)
Parameter \(k\):
Vertical Shift. If \(k > 0\), shifts _____________. If \(k < 0\), shifts _____________.
Parameter \(h\):
Horizontal Shift. If \(h > 0\), shifts _____________. If \(h < 0\), shifts _____________.
Parameter \(a\) (sign):
Reflection. If \(a\) is negative, the graph is _____________ over the x-axis.
Parameter \(a\) (magnitude):
Stretch/Compress. If \(|a| > 1\), vertical _____________. If \(0 < |a| < 1\), vertical _____________.
Blueprint Build Quiz Blueprint Build
Unit Quiz: Linear, Exponential & Transformations
Name: __________________________
Date: ___________________________
Part 1: Identifying Models
Classify each table or description as Linear, Quadratic, or Exponential.
1
Table A
<table class="w-full text-center border-collapse border border-slate-300 text-sm"><tbody><tr class="bg-slate-100"><th class="border border-slate-300 p-1">x</th><td class="border border-slate-300 p-1">0</td><td class="border border-slate-300 p-1">1</td><td class="border border-slate-300 p-1">2</td><td class="border border-slate-300 p-1">3</td></tr><tr><th class="border border-slate-300 p-1">y</th><td class="border border-slate-300 p-1">3</td><td class="border border-slate-300 p-1">6</td><td class="border border-slate-300 p-1">12</td><td class="border border-slate-300 p-1">24</td></tr></tbody></table>
Model Type: ________________________
2
Relationship B
A water tank starts with 500 gallons and loses 15 gallons every hour.
Model Type: ________________________
Part 2: Constructing Functions
3
Write an exponential function \(f(x) = a(b)^x\) that passes through (0, 4) and (2, 36).
SHOW WORK HERE
Function: \(f(x) = \) ________________________
4
Construct a linear function for the values in this table:
SHOW WORK HERE
Function: \(y = \) ________________________
Part 3: Parameter Analysis
5
Given the parent function \(f(x) = x^2\), describe the transformations in \(g(x) = -2(x + 3)^2 - 5\).
Vertical Shift:
Horizontal Shift:
Reflection:
Stretch/Compression:
6
How does changing \(k\) in \(f(x) = b^x + k\) affect the horizontal asymptote of the graph?
Shift and Slide Exit Tickets Shift & Slide: The Matchmaker
Name: ________________________
Match the function to its transformation:
\(f(x) = 2^x + 5\)
\(f(x) = 2^{(x+5)}\)
\(f(x) = 5(2^x)\)
Options:
A. Horizontal shift left 5
B. Vertical stretch by 5
C. Vertical shift up 5
Formative Assessment A
Shift & Slide: The Builder
Name: ________________________
Write an equation for a linear function that has a slope of -2 and passes through the point (0, 7).
Equation: ____________________________________
Formative Assessment B
Shift & Slide: The Critic
Name: ________________________
Student Claim: "Multiplying a function by -1 always shifts it down 1 unit."
Is the student correct? Explain why or why not using what you know about parameters.
Formative Assessment C
Architect Answer Key Architect Answer Key
Teacher Reference & Solution Guide: Model Mechanics
Model Mashup Key
Linear
Rate: Constant Additive
Table: Common Difference (\(d\))
Visual: Straight line, constant slope
Quadratic
Rate: Changing (Linear rate)
Table: 2nd Difference is common
Visual: Parabola, U-shape, vertex
Exponential
Rate: Constant Multiplicative
Table: Common Ratio (\(r\))
Visual: Curve, asymptotic, rapid growth/decay
Transformation Key:
\(k\): UP (+), DOWN (-); \(h\): RIGHT (+ value in formula like \(x-3\)), LEFT (- value in formula like \(x+3\)); Reflection: Over x-axis; Stretch: \(|a|>1\); Compression: \(0<|a|<1\).
Blueprint Build Quiz Solutions
1. Table A:
Exponential (Ratio = 2)
2. Relationship B:
Linear (Constant rate = -15)
3. Exponential Equation:
Steps: \(a = 4\). \(36 = 4(b)^2 \rightarrow 9 = b^2 \rightarrow b = 3\).
Answer: \(f(x) = 4(3)^x\)
4. Linear Equation:
Steps: Slope \(m = (25-10)/(5-2) = 15/3 = 5\). \(y - 10 = 5(x - 2) \rightarrow y = 5x\).
Answer: \(y = 5x\)
5. \(g(x) = -2(x + 3)^2 - 5\):
Vertical Shift: Down 5
Horizontal Shift: Left 3
Reflection: Yes (over x-axis)
Stretch: Vertical stretch by 2
6. Asymptote Analysis:
Changing \(k\) shifts the entire graph vertically. Since the parent exponential function has a horizontal asymptote at \(y=0\), the new asymptote is at \(y = k\).
Shift & Slide Keys
Matchmaker:
\(2^x + 5 \rightarrow\) C
\(2^{(x+5)} \rightarrow\) A
\(5(2^x) \rightarrow\) B
Builder:
\(y = -2x + 7\)
Critic:
Incorrect. Multiplying by -1 is a reflection over the x-axis, not a translation. To shift down 1, you must subtract 1 (\(k = -1\)).
