Graph Boundary Task Cards
DOMAIN & RANGE TASK CARDS
Station Activity & Practice • Cards 1 & 2
Coordinate Analysis
What is the domain and range of this graph?
1
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 -3 -2 -1 1 2 3 4 5
Task Prompts: Find the leftmost and rightmost \(x\)-values for Domain. Find the lowest and highest \(y\)-values for Range.
Record your solution on your Capture Sheet under Task #1.
What is the domain and range of this graph?
2
-3 -2 -1 0 1 2 -1 1 2 3
Pay Attention: Notice the arrow pointing up and to the left! What does an arrow tell you about infinity (\(\infty\))?
Does this curve pass the Vertical Line Test?
DOMAIN & RANGE TASK CARDS
Station Activity & Practice • Cards 3 & 4
Coordinate Analysis
What is the domain and range of this graph?
3
-3 -2 -1 0 1 2 3 4 5 6 -3 -2 -1 1 2 3
Outer Boundaries: Look at the outermost tips of the star along the horizontal and vertical directions.
Is this closed geometric shape a function? Why or why not?
What is the domain and range of this graph?
4
-4 -3 -2 -1 0 1 3 4 -3 -2 -1 1 2 3 4
Tangent Bounds: Find the vertical tangents (left and right edges) and horizontal tangents (top and bottom edges).
Can one \(x\)-input have more than one \(y\)-output on this oval?
DOMAIN & RANGE TASK CARDS
Station Activity & Practice • Cards 5 & 6
Coordinate Analysis
What is the domain and range of this graph?
5
-4 -3 -2 -1 0 1 2 3 4 -2 -1 1 2 3 4
Different Endpoints: Compare the two endpoints: one reaches \(x = -4\) while the other stops at \(x = -1\). What is the true minimum \(x\)?
Does this graph open horizontally or vertically?
What is the domain and range of this graph?
6
-3 -2 -1 0 1 2 3 4 -1 1 2 3 4
Vertex & Ray: The graph has a minimum point (vertex) at \((-1, 0)\) and continues upward to the right infinitely.
Does the domain stop on the left? What symbol represents the right side?
DOMAIN & RANGE TASK CARDS
Station Activity & Practice • Cards 7 & 8
Coordinate Analysis
What is the domain and range of this graph?
7
-4 -3 -2 -1 0 1 2 3 4 5 6 -3 -2 -1 1 2 3 4
Vertical Segment: Look closely at \(x = -1\). The graph has a vertical line connecting \(y = -2\) to \(y = 3\). How does this affect function status?
What are the absolute lowest and highest values of \(y\)?
What is the domain and range of this graph?
8
-2 -1 0 1 2 3 -1 1 2 3 4
Parabolic Minimum: The lowest point is the vertex at \((1, 0)\). The right side ends at \(x = 2\), while the left side continues upwards without bound.
Is the range bounded below, above, or both?
DOMAIN & RANGE TASK CARDS
Station Activity & Practice • Cards 9 & 10
Coordinate Analysis
What is the domain and range of this graph?
9
-1 0 1 2 3 -2 -1 1 2
Both Directions: Both arrows point downward and outward infinitely. What does this mean for the domain \(x\)? Where is the maximum \(y\)?
Is the domain all real numbers (\(\mathbb{R}\))?
What is the domain and range of this graph?
10
-4 -3 -2 -1 0 1 2 -1 -2 -3 -4 -5 -6
Asymmetry Alert: The left side stops at a solid dot at \((-4, -6)\), while the right side continues downward forever with an arrow.
Does this graph pass the Vertical Line Test?
Domain Range Capture Sheet
Domain & Range Capture Sheet
COORDINATE PLANE GRAPH ANALYSIS • TASKS 1–10
Name:
Date:
Period:
\(x\)
Domain: Left to Right (horizontal inputs)
\(y\)
Range: Bottom to Top (vertical outputs)
↕
Function? Passes Vertical Line Test
| Task # | Domain (Input: \(x\)) | Range (Output: \(y\)) | Function?
(Y or N) |
| --- | --- | --- | --- |
| 1 | | | |
| 2 | | | |
| 3 | | | |
| 4 | | | |
| 5 | | | |
| 6 | | | |
| 7 | | | |
| 8 | | | |
| 9 | | | |
| 10 | | | |
Mathematical Analysis • Reflection Questions
1. Select one task that was NOT a function. Explain exactly where and why it failed the Vertical Line Test:
2. When a graph includes an arrow (like Tasks 2, 6, 8, 9, or 10), how does that change your domain or range notation?
