The set of ordered pairs represents a function.
(0, 2), (1, 3), (2, 4), (3, 5), (4, 6)
True
If the above set of ordered pairs is a function, is it a linear or a nonlinear function?
The set of ordered pairs was not a function.
The set of ordered pairs is a linear function.
The set of ordered pairs is a nonlinear function.
The set of ordered pairs is neither a linear nor nonlinear function.
The set of ordered pairs represents a linear function since there is a constant rate of change between each pair.
To determine if the set of ordered pairs represents a linear or a nonlinear function, we can check if there is a constant rate of change between the x-values and y-values.
Let's calculate the rate of change between consecutive ordered pairs:
From (0, 2) to (1, 3), the rate of change is: (3 - 2)/(1 - 0) = 1/1 = 1
From (1, 3) to (2, 4), the rate of change is: (4 - 3)/(2 - 1) = 1/1 = 1
From (2, 4) to (3, 5), the rate of change is: (5 - 4)/(3 - 2) = 1/1 = 1
From (3, 5) to (4, 6), the rate of change is: (6 - 5)/(4 - 3) = 1/1 = 1
Since the rate of change is constant (1) between all the points, the set of ordered pairs represents a linear function.
To determine if the given set of ordered pairs represents a function, we need to check if each input (x-value) corresponds to exactly one output (y-value). If each input has a unique output, then it is a function.
Let's analyze the given set of ordered pairs:
(0, 2), (1, 3), (2, 4), (3, 5), (4, 6)
In this case, each input value (x) is unique, and it is paired with only one output value (y). Therefore, the given set of ordered pairs represents a function.
Now, to determine if this function is linear or nonlinear, we need to examine the pattern formed by the inputs and outputs. If the outputs can be expressed as a linear equation (in the form y = mx + c, where m and c are constants), then it is a linear function. Otherwise, it is a nonlinear function.
Looking at the given set of ordered pairs, we can observe that by increasing the x-value by 1, the y-value increases by exactly 1 each time. This indicates a consistent, linear relationship between the inputs and outputs. Thus, the given set of ordered pairs represents a linear function.