Intervention Blueprint Teacher Guide Intervention Blueprint
Teacher Guide: Function Face-Off (HS.F-IF.C.7)
Standard HS.F-IF.C.7
Lesson Objective
Students will identify, graph, and describe key features of linear, quadratic, square root, and exponential functions using graphing calculators and scaffolded organizers.
Targeted Skills
Distinguishing between function families by equation form.
Using TI-84/Desmos for table and graph exploration.
Identifying intercepts, domain, range, and end behavior.
Pacing Guide (45 Min)
Warm-Up 5 min
Calculator Discovery 15 min
Key Feature Hunt 10 min
Match-Up Mania 10 min
Exit Ticket 5 min
Common Misconceptions
The "Square Root" Stall
Students often try to graph negative x-values and get confused by the calculator error. Fix: Focus on domain restrictions immediately.
Exponential Growth vs. Linear
Students may think a steep line is exponential. Fix: Compare constant rate of change vs. constant ratio in tables.
Strategic Questioning
"Looking at the table, how is the 'y' value changing? Is it adding or multiplying?"
"Where does the graph 'start' or 'stop'? What does that tell us about the domain?"
"If we change this \(+2\) to a \(-2\), how do you predict the graph will move?"
Intervention Roadmap
1
Identify
Use the parent function cheat sheet to name the type.
2
Explore
Enter in calculator. Adjust window to see "whole picture".
3
Anchor
Plot 3-5 critical points from the table.
4
Describe
State domain, range, and intercepts.
Progress Monitoring: Match-Up Mania
Evidence Level Student Action Next Step Beginning Cannot distinguish between curves (quadratic vs. exponential). Flashcards for equation structure; focus on "the square" vs "the exponent". Developing Matches graphs but struggles to identify domain/range from visual. Use "Boundary Box" strategy: Draw a box around the graph to find limits. Proficient Accurately matches and describes features for all 4 types. Introduce basic transformations (h, k) and predict movements.
Materials Checklist
TI-84 or Desmos Access
Function Galaxy Worksheets
Match-Up Mania Card Sets
Colored pencils (for graphing)
Function Face-Off Slides Tier 2 Intervention
Function Face-Off
Mastering Graphing, Key Features, and Function Families
Goal: HS.F-IF.C.7
The "Fantastic Four"
Linear
f(x) = mx + b
Quadratic
f(x) = x²
Sq. Root
f(x) = √x
Exponential
f(x) = abˣ
Calculator Power Moves
1
Y= Menu
Type your equation carefully. Use parentheses for exponents!
2
Zoom 6 (Standard)
Always start with a standard 10x10 window.
3
2nd + Graph (Table)
Find your anchor points. Look for whole numbers!
Troubleshooting
"ERR: INVALID DIM" → Turn off your Stat Plots!
"Blank Screen" → Check your window settings or equation.
What are we looking for?
Intercepts
x-intercept: Where the graph hits the horizontal axis (y=0).y-intercept: Where the graph hits the vertical axis (x=0).
Domain & Range
Domain: All possible x-values (left to right).Range: All possible y-values (bottom to top).
Visual Guide
Vertex / Min
Intercepts
Match-Up Mania
Time to test your skills! Work with your partner to match the Equation to the Graph and Table .
Equation
Find the Family
Graph
Check the Shape
Table
Verify the Points
Graphing Galaxy Worksheet Graphing Galaxy
Function Family Exploration & Guided Graphing
Name:
Date:
1
Function Identification
Identify the function family based on the equation form.
A) \(f(x) = 3x - 5\)
B) \(g(x) = x^2 + 4x + 2\)
C) \(h(x) = \sqrt{x+3}\)
D) \(k(x) = 2^x\)
2
Graph Discovery: The Quadratic
Equation: \(y = x^2 - 4x + 3\)
Press [Y=] and enter the equation.
Press [2nd] then [Graph] for the table.
Find the points below.
Sketch your graph above.
Vertex:
y-intercept:
Domain:
Range:
3
The "Curious" Square Root
Equation: \(y = \sqrt{x+4}\)
Look at your table. Why do some values say "ERROR" ?
Where does the graph "start"?
Final Check
Linear Key
Does it have a square or exponent?
Yes No
Range Search
Does the graph go up forever?
Yes No
One Sentence
The biggest difference between Linear and Exponential is...
Match-Up Mania Activity Match-Up Mania
Progress Monitoring Activity
CARDS 12
How to Play
Cut out the cards below. Match the Equation , Graph , and Key Feature for each of the 4 functions. Once you've matched a set of 3, show your teacher!
Equation Card 1
\(y = 2x - 3\)
Equation Card 2
\(y = x^2 - 1\)
Equation Card 3
\(y = 2^x\)
Graph Card A
Graph Card B
Graph Card C
Feature Card X
Has a constant rate of change; Domain & Range are all real numbers.
Feature Card Y
Has a vertex at (0, -1); Symetrical shape.
Feature Card Z
Grows very slowly at first, then increases rapidly; never touches the x-axis.
Final Set: Square Root
Equation Card 4
\(y = \sqrt{x} + 2\)
Graph Card D
Feature Card W
Domain is \(x \geq 0\); Curve starts at a specific point and continues in one direction.
