Graph Hunters Worksheet
GRAPH HUNTERS Guided Practice
Mastering Domain, Range, Intercepts, & Function Values
Name:
Date:
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Interval Notation & Features Quick Ref
Domain (x-values)
Scan left-to-right. Write the x-interval covered.
Range (y-values)
Scan bottom-to-top. Write the y-interval covered.
Interval Notation
[ , ] Solid (included)
( , ) Open / \(\pm\infty\)
Intercepts & f(a)
x-int: where \(y=0\)
y-int: where \(x=0\)
Guided Walkthrough Example Read This First!
x y 2 4 -2 -4 2 4 -2
1. Domain: Scan left \((x = -4)\) to right \((x = 2)\). Left is solid (included), right is open (excluded). Domain: \([-4, 2)\)
2. Range: Scan bottom \((y = -2)\) to top \((y = 4)\). Bottom is solid (included), top is open (excluded). Range: \([-2, 4)\)
3. Intercepts: Crosses x-axis at \((-2, 0)\). Crosses y-axis at \((0, 2)\).
4. Evaluating: To find \(f(-1)\), look at \(x = -1\). The vertical height of the line is \(1\). So, \(f(-1) = 1\).
Problem 1: Guided Practice
Analyze the graph and answer the prompts below.
x y 2 4 -2 -4 2 -2
A. Domain (left-to-right)
What is the furthest left x-value? ______. Is it included? (Yes/No) ______
What is the furthest right x-value? ______. Is it included? (Yes/No) ______
Domain in Interval Notation:
B. Range (bottom-to-top)
What is the lowest y-value on the entire graph? ______
What is the highest y-value on the entire graph? ______
Range in Interval Notation:
C. Find the Intercepts
Where does the graph cross the x-axis?
List as coordinate points: ________________________
Where does the graph cross the y-axis?
List as coordinate point: ________________________
x-intercepts
y-intercept
D. Evaluate Function Values
To find \(f(-1)\), look at \(x = -1\). Follow it vertically to find the graph's y-value: ______
Now find \(f(2)\). Follow \(x = 2\) vertically to find the y-value: ______
\(f(-1)\)
\(f(2)\)
Unit: Functions & Graphs Page 1 of 2 Instructional Activity Worksheet
GRAPH HUNTERS Independent Practice
Apply your skills to find domain, range, intercepts, and function values.
Page 2
Problem 2: Line Segment x y 2 4 -2 -4 2 -2 -4
Left is open, Right is solid.
Find each feature for the line segment shown on the left. Write all intervals using interval notation.
Domain
Range
x-intercept
y-intercept
Evaluate: \(f(-1)\)
Evaluate: \(f(-3)\)
Problem 3: Infinite Ray x y 2 -2 2 -2
Arrow goes to \(\infty\).
Find each feature for the ray shown on the left. Write all intervals using interval notation.
Domain
Range
x-intercept
y-intercept
Evaluate: \(f(1)\)
Evaluate: \(f(3)\)
Metacognitive Check-In
Explain in your own words the difference between using a bracket [ ] and a parenthesis ( ) in interval notation. How do you know which one to choose by looking at a graph's endpoint?
Unit: Functions & Graphs Page 2 of 2 Instructional Activity Worksheet
Graph Hunters Teacher Guide
GRAPH HUNTERS Teacher Guide & Facilitation Plan
Scaffolded Instructional Strategies for Domain, Range, and Key Features
Teacher Resource
Lesson Goal
This lesson is engineered to target student weaknesses in identifying domain and range of continuous functions using interval notation. By isolating boundary scanning from piecewise algebraic formulas, students build foundational graph literacy.
Lesson Elements
- Guided Practice Worksheet (Pages 1 & 2)
- Additional Practice Worksheet (Page 3)
- Metacognitive Self-Checklist
Suggested Pacing (50-Minute Block)
PHASE
WHAT STUDENTS & TEACHERS ARE DOING
TIME
Warm-Up & Notes
Review Cheat Sheet on Worksheet Page 1. Walk through the guided example as a class, modeling horizontal/vertical pencil scans.
10 min
Guided Practice
Students solve Problem 1. Teacher monitors bracket vs. parenthesis usage on solid/open endpoints.
10 min
Independent Work
Students solve Problems 2 and 3 on Worksheet Page 2. Emphasize Problem 3's infinite boundary and check the concept tips.
10 min
Additional Practice
Students solve Problems 4 and 5 on the Practice Worksheet. This sheet focuses heavily on curved segments and infinite rays.
15 min
Reflect & Debrief
Review Metacognitive prompt and Boundary Self-Checklist. Call on groups to share their checklist insights. Collect for assessment.
5 min
Critical Student Misconceptions to Watch For
1. Top-to-Bottom Range Scanning
Students write Range from the top point down (e.g., \([4, -2]\) instead of \([-2, 4]\)). Remind them: Intervals are written from least to greatest (bottom to top).
2. Confusing Intercept coordinates
Students often write the x-intercept as \((0, a)\) instead of \((a, 0)\). Intervention: Clarify that on the x-axis, the vertical height (\(y\)) must be \(0\).
3. Including Infinity in Brackets
Students write \([ -2, \infty ]\) with a square bracket. Explain: Since we can never reach infinity, we must always use parenthesis \((\infty)\).
4. Evaluating Function Values
When evaluating \(f(a)\), students often guess or solve algebraically. Guided cue: "Go to \(x = a\) on the x-axis, go vertically to the graph, and read the height."
Graph Hunters Practice Worksheet
GRAPH HUNTERS Additional Practice
Extra practice for domain, range, intercepts, and function values.
Name:
Date:
Pd:
Review Interval Notation: Use brackets [ ] for included numbers (solid dots) and parentheses ( ) for excluded numbers (open dots, infinity).
Problem 4: Curved Segment x y 2 -2 2 4 -2 -4
Note open/solid ends.
Analyze the curved segment graph above and solve for each feature:
Domain (Interval Notation)
Range (Interval Notation)
x-intercepts
y-intercept
Evaluate Function: \(f(2)\)
Problem 5: Infinite Ray x y 2 -2 -4 2 -2
The arrow goes to infinity!
Analyze the infinite ray graph above and solve for each feature:
Domain (Interval Notation)
Range (Interval Notation)
x-intercept
y-intercept
Evaluate Function: \(f(1)\)
Domain & Range Boundary Self-Check
Before turning in your work, check these common items:
Did I write intervals from least to greatest (left-to-right for Domain, bottom-to-top for Range)?
Did I use parentheses ( ) for open dots and infinity \(\infty\)?
Unit: Functions & Graphs Additional Practice Worksheet Page 1 of 1
