Function Family Worksheet Parent Function Power
The Core 10 Master List & Field Notes
Name:
Date:
Jan 19, 2026
1. Warm-Up: Mystery Graphs
Look at the unlabeled graphs on the screen. Sketch them quickly below and guess their parent equations.
Equation 1:
Equation 2:
Equation 3:
2. The Core 10 Master Table
Video Segment: 0:00 - 14:42
Function Name & Eq. Sketch (with Intercepts) Domain (Interval) Range (Interval) Linear \(y = x\) Quadratic \(y = x^2\)
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| Cubic
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| Square Root
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Function Name & Eq. Sketch Domain Range Cube Root \(y = \sqrt[3]{x}\) Absolute Value \(y = x \)
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| Rational
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| Inverse Square
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| Exponential
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| Natural Log
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3. Gallery Walk Observations
Identify a function that has a VERTICAL ASYMPTOTE. What causes it? (Write the equation and the reason)
Which two functions are reflections of each other across the line \(y = x\)?
BIG QUESTION: Why is the domain of \(y = \sqrt{x}\) restricted to \([0, \infty)\) while \(y = \sqrt[3]{x}\) is all real numbers?
Parent Power Slides Parent Function
Power
Mastering the Core 10
11TH GRADE PRE-CALCULUS UNIT 1: FUNCTIONS
Warm-Up: Mystery Graphs
On your worksheet, sketch these 3 shapes and guess their parent equations.
Graph A
Graph B
Graph C
The Reveal
A
Linear Function
\(y = x\)
B
Quadratic Function
\(y = x^2\)
C
Absolute Value Function
\(y = |x|\)
Video Field Guide
1
Watch carefully as we explore the **Core 10** parent functions.
2
We will **pause after each function**.
3
Update your table with the **Sketch, Domain, and Range**.
Ready your pencils!
Embedded media
Watching: Basic Overview & Graphing Parent Functions | Stop at: 14:42
Function Family Gallery
Your Group Mission:
Create a visual poster for your assigned function.
Make it **BIG**, **BOLD**, and **COLORED**.
Ensure all "Key Features" are included.
Assigned Groups:
1. Rational
2. Cubic
3. Square Root
4. Cube Root
5. Exponential
6. Natural Log
Poster Requirements
Parent Equation & Name
Large Accurate Sketch
Domain & Range (Interval)
Key Features Asymptotes, Intercepts, or Symmetry
"Make your graph the star of the show. If there's an asymptote, draw it as a dashed line!"
Gallery Walk
🤫
Quiet Reflection
Move silently through the posters.
📝
Capture Notes
Complete Section 3 of your worksheet.
🕵️♂️
Look for Patterns
What do similar functions have in common?
TIME: 5 MINUTES
Final Reflection
"If you could only remember **one** thing about parent functions for tomorrow's transformation lesson, what would it be?"
Turn in your worksheets as you exit!
Poster Master Teacher Guide Teacher Guide: Poster Master
Parent Function Power
PRE-CALCULUS | LESSON 1
Lesson Flow & Pacing
5 min **Warm-Up**: Do not provide answers immediately. Let students struggle with the V-shape vs. U-shape distinction.
15 min **Video**: Pause at: 2:00, 3:15, 4:10, 5:10, 6:05, 6:58, 8:43, 11:37, 12:25, 14:42.
20 min **Activity**: Circulate during poster creation. Check for horizontal vs. vertical asymptotes specifically.
5 min **Closure**: Use the Gallery Walk for peer-to-peer correction. If they see a mistake, they should write a sticky note!
Misconception Alert
**The "U" vs "V"**: Students often confuse \(y = x^2\) and \(y = |x|\). Emphasize that \(x^2\) is a curve (rate of change varies) while \(|x|\) is linear (rate of change is constant \(\pm 1\)).
**Asymptote Anxiety**: Students may think a graph *cannot* touch an asymptote. Remind them that for \(1/x\), the value literally cannot exist (division by zero).
**Brackets vs Parens**: Check that they use \([0, \infty)\) for Square Root but \((0, \infty)\) for Natural Log and Exponential.
Answer Key: The Core 10 Master Table
Function Equation Domain Range Key Feature to Check Linear y = x \((-\infty, \infty)\) \((-\infty, \infty)\) Passes through (0,0) Quadratic y = x² \((-\infty, \infty)\) \([0, \infty)\) Vertex at (0,0) Cubic y = x³ \((-\infty, \infty)\) \((-\infty, \infty)\) "S" shape through origin Square Root y = √x \([0, \infty)\) \([0, \infty)\) Endpoint at (0,0) Cube Root y = ³√x \((-\infty, \infty)\) \((-\infty, \infty)\) Inflection point at (0,0) Absolute Value y = x \((-\infty, \infty)\) Rational y = 1/x \((-\infty, 0) \cup (0, \infty)\) \((-\infty, 0) \cup (0, \infty)\) H.A. y=0, V.A. x=0 Inv. Square y = 1/x² \((-\infty, 0) \cup (0, \infty)\) \((0, \infty)\) Symmetric over y-axis Exponential y = e^x \((-\infty, \infty)\) \((0, \infty)\) y-intercept at (0,1) Natural Log y = ln(x) \((0, \infty)\) \((-\infty, \infty)\) x-intercept at (1,0)
Poster Activity Rubric
Criteria Mastery (5 pts) Developing (3 pts) Needs Work (1 pt) Accuracy Graph is perfectly sketched with correct intercepts/asymptotes. Shape is correct, but details (intercepts/asymptotes) are slightly off. Incorrect parent shape used. Domain/Range Interval notation is 100% correct, including brackets/parens. Correct values, but misuse of brackets vs. parentheses. Incorrect domain or range values. Visual Impact Large, readable from 10 feet, uses multiple colors. Readable, but small or lacks color contrast. Difficult to read; messy or incomplete.
Group Assignments & Complexity
Assign functions based on group confidence levels:
Confidence Level: 1
Cubic / Linear
Very straightforward domain/range.
Confidence Level: 2
Sq. Root / Exp / Abs Value
Introduces restricted domains or intercepts.
Confidence Level: 3
Rational / Natural Log
Requires union notation and V.A. awareness.
Worksheet: Gallery Walk Answers
Q1: Vertical Asymptote?
\(y=1/x\), \(y=1/x^2\), \(y=\ln(x)\). Caused by values where the function is undefined (denominator = 0 or log of non-positive).
Q2: Reflections over \(y=x\)?
\(y=e^x\) and \(y=\ln(x)\). They are inverse functions.
Q3: Why is root domain different?
Square root index is even (2), so you cannot take the square root of a negative without entering imaginary numbers. Cube root index is odd (3), and negative numbers have real cube roots (e.g., \(\sqrt[3]{-8} = -2\)).
