The set of ordered pairs shown is a function. {(0, -1), (2, 5), (-3, -10), (-1, -4), (1, 2)} Which of the following represents the same function as the ordered pairs?
y = 3 x - 1
To determine which of the given options represents the same function as the ordered pairs {(0, -1), (2, 5), (-3, -10), (-1, -4), (1, 2)}, we need to find the rule or pattern followed by the input-output pairs.
Looking at the ordered pairs, we can see that the first element (x-value) of each pair is different, meaning that each x-value is mapped to a unique y-value.
Let's write down all the x-values and their corresponding y-values:
(0, -1)
(2, 5)
(-3, -10)
(-1, -4)
(1, 2)
From this, we can see that:
0 is mapped to -1
2 is mapped to 5
-3 is mapped to -10
-1 is mapped to -4
1 is mapped to 2
Now, let's compare this pattern to the options provided. Unfortunately, the options are not provided in the question. Please provide the options, and I will guide you further.
To find which of the given options represents the same function as the ordered pairs, we can first understand what makes the given set of ordered pairs a function.
A set of ordered pairs is a function if each input (x-coordinate) is associated with exactly one output (y-coordinate). This means that for each x-coordinate, there should not be more than one y-coordinate associated with it.
Let's analyze each option:
A) {(0, -1), (1, 2), (2, 5), (-1, -4), (-3, -10), (3, 7)}
B) {(0, -1), (2, 5), (-3, -10), (-1, -4), (1, 2), (3, 7)}
C) {(0, -1), (2, 5), (-3, -10), (-1, -4), (1, 2)}
D) {(0, -1), (2, 5), (-3, -10), (-1, -4), (1, 2), (1, 7)}
Looking at option A, we can see that (3, 7) has been added to the set. This means that the input x = 3 now has two associated y-coordinates: 5 and 7. This violates the definition of a function since x = 3 should only have one y-coordinate.
Option B is just the same as the original set of ordered pairs, so it represents the same function.
Option C is the same as the original set of ordered pairs, so it represents the same function.
Looking at option D, we can see that (1, 7) has been added to the set. This means that the input x = 1 now has two associated y-coordinates: 2 and 7. This violates the definition of a function since x = 1 should only have one y-coordinate.
Therefore, the options that represent the same function as the original set of ordered pairs are B and C.