To determine which graph represents a function, you need to verify that each \( x \)-value in the set of ordered pairs maps to exactly one \( y \)-value. This means that for each \( x \)-value, there should be only one corresponding \( y \)-value.
Let's analyze each set of ordered pairs:
1. **(negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5)**
- Here, the \( x \)-value 2 maps to both \( -1 \) and \( -3 \). Hence, this is **not** a function.
2. **(negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4)**
- Here, the \( x \)-value 4 maps to both \( -3 \) and \( 4 \). Hence, this is **not** a function.
3. **(negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1)**
- Every \( x \)-value has a unique \( y \)-value:
- \( x = -3 \) maps to \( 2 \)
- \( x = -2 \) maps to \( 2 \)
- \( x = 0 \) maps to \( 1 \)
- \( x = 1 \) maps to \( 3 \)
- \( x = 2 \) maps to \( -4 \)
- \( x = 4 \) maps to \( -1 \)
- This set represents a function because each \( x \)-value is associated with exactly one \( y \)-value.
4. **(negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5)**
- Here, the \( x \)-value -2 maps to both \( 1 \) and \( -1 \), and the \( x \)-value 0 maps to both \( -2 \) and \( -4 \). Hence, this is **not** a function.
Therefore, the only set of ordered pairs that represent a function is the third set:
**(negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1)**.
Which graph shows a set of ordered pairs that represent a function?
On a coordinate plane, solid circles appear at the following points: (negative 2, 3), (negative 1, 2), (1, 1), (2, negative 1), (2, negative 3), (4, negative 5).
On a coordinate plane, solid circles appear at the following points: (negative 4, negative 4), (negative 2, 2), (1, 1), (2, negative 5), (4, negative 3), (4, 4).
On a coordinate plane, solid circles appear at the following points: (negative 3, 2), (negative 2, 2), (0, 1), (1, 3), (2, negative 4), (4, negative 1).
On a coordinate plane, solid circles appear at the following points: (negative 4, 2), (negative 2, 1), (negative 2, negative 1), (0, negative 2), (0, negative 4), (2, negative 5).
1 answer
1 answer