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 | | | |
| \(y = x^2\) | | | |
| | |
| Cubic
\(y = x^3\) |
| | |
| Square Root
\(y = \sqrt{x}\) |
| | |
| Function Name & Eq. | Sketch | Domain | Range |
|---|
| Cube Root | | | |
| \(y = \sqrt[3]{x}\) | | | |
| | | |
| Absolute Value | | | |
| \(y = | x | \) | |
| | |
| Rational
\(y = 1/x\) |
| | |
| Inverse Square
\(y = 1/x^2\) |
| | |
| Exponential
\(y = e^x\) |
| | |
| Natural Log
\(y = \ln(x)\) |
| | |
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 |
