To solve this problem, we need to
identify whether each graph represents a function. We use the
Vertical Line Test to determine this.
---
🔍 Vertical Line Test:
A graph represents a
function if
no vertical line intersects the graph more than once.
If any vertical line crosses the graph at two or more points, then it is
not a function.
Let’s go through each graph one by one:
---
1)
- This is a straight line (linear).
- A vertical line will intersect it only once.
✔ Function
>
Answer: Function
---
2)
- This is a parabola opening upward.
- It's symmetric about the y-axis.
- Any vertical line will cross it at most once.
✔ Function
>
Answer: Function
---
3)
- This is a wavy curve (like a cubic or higher-degree polynomial).
- Even though it curves up and down, no vertical line crosses it more than once.
✔ Function
>
Answer: Function
---
4)
- This graph looks like a sideways "U" or a horizontal parabola.
- For example, at x = 0, there are
two y-values (one above and one below).
- A vertical line at x = 0 would intersect the graph
twice.
✘ Not a function
>
Answer: Not a function
---
5)
- This graph has a loop or a zigzag shape.
- Look near x = -1: you can draw a vertical line that hits the graph at
three points.
- So, multiple outputs for one input.
✘ Not a function
>
Answer: Not a function
---
6)
- This is a set of connected line segments going from left to right.
- Each x-value maps to only one y-value.
- No vertical line crosses more than once.
✔ Function
>
Answer: Function
---
7)
- This is a
sideways parabola, opening to the left.
- For example, at x = -2, there are
two y-values (top and bottom).
- Vertical line test fails.
✘ Not a function
>
Answer: Not a function
---
8)
- This is another sideways U-shape, opening to the right.
- At x = 2, there are two y-values (one at y=1 and one at y=-1).
- Vertical line at x=2 intersects twice.
✘ Not a function
>
Answer: Not a function
---
✔ Final Answers:
| Graph | Function? |
|-------|-----------|
| 1) | Yes |
| 2) | Yes |
| 3) | Yes |
| 4) | No |
| 5) | No |
| 6) | Yes |
| 7) | No |
| 8) | No |
---
📝 Summary:
Use the
Vertical Line Test:
- If every vertical line intersects the graph
at most once, it’s a function.
- Otherwise, it's
not a function.
---
✔ Correct Answers to Fill In:
1)
Function
2)
Function
3)
Function
4)
Not a function
5)
Not a function
6)
Function
7)
Not a function
8)
Not a function
Let me know if you'd like explanations with specific coordinates!
Parent Tip: Review the logic above to help your child master the concept of identifying graphs of functions worksheet.
