To determine whether each graph represents a
function, we use the
Vertical Line Test.
🔍 Vertical Line Test:
A graph represents a
function if
no vertical line intersects the graph more than once.
In other words, for every input (x-value), there must be
at most one output (y-value).
Let’s analyze each graph:
---
✔ Graph 1
- Shape: A sideways parabola (opening to the right).
- Observation: For some x-values (e.g., x = 0), there are
two y-values (top and bottom of the curve).
- Vertical line at x = 0 would intersect the graph
twice.
-
✘ Not a function
>
Answer: No
---
✔ Graph 2
- Shape: A straight diagonal line (linear).
- Observation: Every vertical line will cross the graph
only once.
- Each x has exactly one y.
-
✔ Is a function
>
Answer: Yes
---
✔ Graph 3
- Shape: Discrete points.
- Observation: All x-values are different; no two points share the same x-coordinate.
- Even though it's not connected, each x maps to only one y.
-
✔ Is a function
>
Answer: Yes
---
✔ Graph 4
- Shape: Two horizontal line segments with open and closed circles.
- Left segment: from (-2, -4) to (-1, -4), closed on left, open on right.
- Right segment: from (0, 2) to (1, 2), open on left, closed on right.
- Observation:
- At x = -1: point is
open, so not included.
- At x = 0: point is
open, so not included.
- No x-value appears more than once.
- So, each x has only one y.
-
✔ Is a function
>
Answer: Yes
---
✔ Graph 5
- Shape: Scattered points.
- Observation: All points have
unique x-values (no two points share the same x).
- Even if they were close, as long as no x repeats, it's a function.
-
✔ Is a function
>
Answer: Yes
---
✔ Graph 6
- Shape: A circle centered at origin.
- Observation: For many x-values (e.g., x = 0), there are
two y-values (top and bottom of circle).
- Vertical line through center crosses circle at two points.
-
✘ Not a function
>
Answer: No
---
✔ Final Answers:
| Graph | Function? |
|-------|-----------|
| 1 |
No |
| 2 |
Yes |
| 3 |
Yes |
| 4 |
Yes |
| 5 |
Yes |
| 6 |
No |
---
📝 Summary:
Use the
vertical line test:
- If any vertical line crosses the graph
more than once →
Not a function
- If every vertical line crosses
at most once →
It is a function
✔ Functions: Graphs 2, 3, 4, 5
✘ Not functions: Graphs 1, 6
Parent Tip: Review the logic above to help your child master the concept of functions vertical line test worksheet.
