Function Families Adapted Worksheet
Algebra 1 Support Modified Packet
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Date:
The 5 Function Families: Match the Shapes
Every function equation has a special shape when you graph it!
Visual Cheat Sheet
Look at the Clue Symbol & Shape:
Linear
\( y = x \)
Straight Line
Quadratic
\( y = x^2 \)
U-Shape
Absolute Value
\( y = |x| \)
V-Shape
Square Root
\( y = \sqrt{x} \)
Curved Hook
Exponential
\( y = 2^x \)
Hockey Stick
Warm-Up Activity
Circle the Matching Shape:
Problem 1
\( y = |x| \)
Notice the straight bars | | around \( x \)!
Which shape?
V-Shape (Sharp point)
Straight Line (Linear)
Problem 2
\( y = x^2 \)
Notice the small 2 exponent!
Which shape?
Curved Hook (Square root)
U-Shape (Parabola)
Problem 3
\( y = \sqrt{x} \)
Notice the radical hook symbol \( \sqrt{} \)!
Which shape?
Curved Hook (Starts at a point)
Hockey Stick (Exponential)
Success Rule: Look closely at the equation! The symbol always tells you the shape. No calculations needed!
Algebra 1 • Modified Resource Page 1 of 4: Shapes & Families
Step-by-Step Guide Visual Method
Domain & Range
The 2-Color Highlighter Method
Use colors to clearly see the horizontal domain and vertical range.
X
DOMAIN (Blue)
Horizontal: Left to Right \(\longleftrightarrow\)
Domain looks at the \( x \)-axis. If arrows point both left and right, it covers All Real Numbers!
Y
RANGE (Red)
Vertical: Bottom to Top \(\updownarrow\)
Range looks at the \( y \)-axis. Find the lowest point on the graph and see where it goes!
WORKED MODEL Graph of \( f(x) = 2^x + 1 \) (Exponential)
x y Lowest boundary = 1 (0, 2) (1, 3)
Arrows go left, right, and UP!
1 Reading the Domain (Blue line):
Does the graph stop on the left? No \(\leftarrow\)
Does the graph stop on the right? No \(\rightarrow\)
Domain = All Real Numbers
2 Reading the Range (Red line):
What is the lowest height it touches? It sits just above 1.
Does it go up forever? Yes \(\uparrow\)
Range = \( y > 1 \)
Rule Check (Circle the correct bold word):
1. Domain measures the graph from:
[ Left to Right ] [ Bottom to Top ]
2. Range measures the graph from:
[ Left to Right ] [ Bottom to Top ]
Algebra 1 • Modified Resource Page 2 of 4: The Highlighter Method
Guided Practice Scaffolded Problems
Core Tasks 1 & 2
Finding Boundaries on Pre-Drawn Graphs
The graphs are already plotted for you! Use the numbers to find domain and range.
Problem 1
Function: \( f(x) = \sqrt{x+1} - 4 \) (Square Root)
Hook Curve
y x -1 -4 Start: (-1, -4)
a) Look at the green dot. What is the start point?
( \( x = -1 \) , \( y = -4 \) )
b) Domain (\( x \)-values): Does it go to the right from -1?
\( x \ge -1 \) \( x \le -1 \)
c) Range (\( y \)-values): Does it go UP from -4?
\( y \ge -4 \) \( y \le -4 \)
Problem 2
Function: \( h(x) = |x - 2| \) (Absolute Value)
V-Shape
y x 2 0 Vertex: (2, 0)
a) The sharp point at the bottom is called the:
[ Vertex ] [ Flat line ]
b) Domain: The arrows point left and right forever.
All Real Numbers
c) Range: The lowest \( y \)-value is 0 and it goes UP.
\( y \ge 0 \) \( y \le 0 \)
Algebra 1 • Modified Resource Page 3 of 4: Scaffolded Practice
Show What You Know Quick Check
Score: _____ / 5
Check for Understanding & Exit Ticket
Answer each question by circling the best answer or filling in the number.
Part 1
Quick Recognition
1. Which equation has a U-Shape (Quadratic)?
Look for the exponent 2!
A \( y = (x - 2)^2 \)
B \( y = |x + 2| \)
2. Where does this graph cross the y-axis?
The red dot is at +3:
A (0, 3)
B (3, 0)
EXIT TICKET
Function: \( f(x) = \sqrt{x + 4} \)
Square Root
y x Start: (-4, 0)
Starts at \( x = -4 \) on the x-axis
a) Circle the function family:
[ Square Root ] [ Linear Line ]
b) Domain (Left to Right):
The green start dot is at \( x = -4 \).
Domain: \( x \ge \) -4
c) Range (Bottom to Top):
The lowest height on the y-axis is 0.
Range: \( y \ge \) 0
How do you feel about reading function graphs?
Circle your confidence level:
😊 I got it!
🤔 Getting there
🙋 Need help
Algebra 1 • Modified Resource Page 4 of 4: Exit Ticket & Reflection
Function Families Answer Key
Teacher & Paraprofessional Guide Answer Key • Pages 1 & 2
Unit 3: Lesson 8a Support
Function Families Answer Key & Facilitation Notes
Complete solutions and prompting tips for co-teachers, aides, and educators.
Student Page 1
Function Types & Warm-Up Solutions
3 Items Total
Problem 1 \( y = |x| \)
Shape Choice:
✓ B: Sharp V-Shape
Axis Intercept:
( 0 , 0 )
Problem 2 \( y = x^2 \)
Shape Choice:
✓ A: U-Shape (Parabola)
Axis Intercept:
( 0 , 0 )
Problem 3 \( y = 2^x \)
Shape Choice:
✓ C: Exponential
y-Intercept:
( 0 , 1 )
Student Page 2
The Highlighter Method: Solutions
Concept Check
Rule Check #1 (Domain):
Domain measures the graph from:
✓ [ Left to Right ] [ Bottom to Top ]
Rule Check #2 (Range):
Range measures the graph from:
[ Left to Right ] ✓ [ Bottom to Top ]
Expected Student Understanding for Modeled Graph \( f(x) = 2^x + 1 \):
• Domain: All Real Numbers (arrows point both left & right).
• Range: \( y > 1 \) (curve hovers right above the dashed asymptote at 1).
Paraprofessional & Co-Teacher Prompting Matrix
If student confuses D & R:
Say: "Remember Dr. X-Ray! D comes first like X. R comes second like Y."
If student cannot find Intercept:
Have them take their index finger and trace down the vertical y-axis until they run into the line.
Physical Highlighters:
Provide a blue and red marker. Physically highlight the x-axis blue and the y-axis red before starting!
Function Families • Teacher Answer Key Page 1 of 2
Teacher & Paraprofessional Guide Answer Key • Pages 3 & 4
Core Tasks & Exit Ticket
Core Tasks & Exit Ticket Solutions
Accurate solutions, common misconceptions, and grading criteria.
Student Page 3
Core Tasks 1 & 2 Answer Key
Guided Practice
Task 1: \( f(x) = \sqrt{x+1} - 4 \) Square Root
a) Start Point: ( \( x = \) -1 , \( y = \) -4 )
