To determine whether each graph represents a
function, we use the
Vertical Line Test:
>
Vertical Line Test: If any vertical line intersects the graph at more than one point, then the graph does
not represent a function. If every vertical line intersects the graph at most once, then it
does represent a function.
Let’s go through each graph one by one:
---
1)
- The graph is a
curve that opens to the right, like a sideways parabola.
- A vertical line (e.g., at $ x = 0 $) will intersect the graph at
two points.
-
✔ Not a function
---
2)
- This is a smooth curve with peaks and valleys (like a wave).
- Any vertical line will cross the graph at
only one point.
-
✔ It is a function
---
3)
- This is a
parabola opening upward, vertex at the bottom.
- Every vertical line crosses the graph at only
one point.
-
✔ It is a function
---
4)
- This graph looks like a
sideways "S" shape, possibly part of a cubic or other relation.
- At some $ x $-values (e.g., near $ x = 0 $), a vertical line would pass through
two points.
-
✔ Not a function
---
5)
- This is a
straight diagonal line going from top-left to bottom-right.
- A vertical line will intersect it at
exactly one point.
-
✔ It is a function
---
6)
- This is an
ellipse (oval shape).
- A vertical line through the center (e.g., $ x = 0 $) will intersect the graph at
two points.
-
✔ Not a function
---
7)
- This graph has two separate curves: one on the left and one on the right.
- Both are downward-opening curves.
- For example, at $ x = -1 $, there are
two y-values (top and bottom parts).
-
✔ Not a function
---
8)
- This is a
V-shaped graph, resembling an absolute value function.
- It's symmetric about the y-axis but still passes the vertical line test.
- Each $ x $ maps to exactly one $ y $.
-
✔ It is a function
---
9)
- This graph consists of
two horizontal lines (a solid line at $ y = 2 $ from $ x = 0 $ to $ x = 10 $, and another at $ y = 20 $ from $ x = 0 $ to $ x = 10 $).
- Wait — actually, looking closely: There are
two separate horizontal segments at different $ y $-values, both over the same $ x $-interval.
- So for any $ x $ between 0 and 10, there are
two outputs ($ y = 2 $ and $ y = 20 $).
-
✔ Not a function
---
✔ Final Answers:
| Graph | Is it a function? |
|-------|-------------------|
| 1) |
✘ No |
| 2) |
✔ Yes |
| 3) |
✔ Yes |
| 4) |
✘ No |
| 5) |
✔ Yes |
| 6) |
✘ No |
| 7) |
✘ No |
| 8) |
✔ Yes |
| 9) |
✘ No |
---
Summary:
- Use the
vertical line test.
- If a vertical line hits the graph
more than once, it's
not a function.
- Only graphs
2, 3, 5, and 8 pass the test.
✔ Functions:
2, 3, 5, 8
✘ Not functions:
1, 4, 6, 7, 9
Parent Tip: Review the logic above to help your child master the concept of horizontal line test worksheet.
