- A
relation shows a relationship between two values.
- A function is a
relation that pairs each
input with
exactly one output.
Determine if each relation is a function:
1. `{(-13, 4), (7, -15), (-13, 9), (6, -12), (-18, 0)}`
-
Not a function
- Notes: The input `-13` has two different outputs (`4` and `9`). A function must have exactly one output per input.
2. `{(6, 0), (-12, -16), (-6, 10), (20, -7)}`
-
Function
- Notes: Each input has exactly one output. No repeated inputs.
3. `y = x² - 1`
-
Function
- Notes: For every input `x`, squaring it and subtracting 1 gives exactly one output `y`.
4. Table:
```
x y
9 -18
-20 0
-6 1
-17 16
9 17
11 19
```
-
Not a function
- Notes: The input `9` appears twice with different outputs (`-18` and `17`). This violates the definition of a function.
5. Table:
```
x y
-13 2
-10 8
-8 3
12 -9
16 7
18 -2
```
-
Function
- Notes: All inputs are unique, so each input maps to exactly one output.
6. Graph (line passing through origin with positive slope)
-
Function
- Notes: It passes the vertical line test — any vertical line intersects the graph at most once.
7. Graph (circle centered at origin)
-
Not a function
- Notes: Fails the vertical line test — many vertical lines intersect the circle at two points, meaning one input `x` corresponds to two outputs `y`.
Parent Tip: Review the logic above to help your child master the concept of relations and functions worksheet pdf.
