Is the table a linear function or nonlinear function?
x: -2, -1, 0, 1, 2
y: 16, 20, 24, 28, 32
A: Linear
B: Nonlinear
To determine whether the given table represents a linear or nonlinear function, we need to analyze the pattern between the x-values and y-values.
To check for linearity, we can calculate the differences between consecutive y-values and see if they are constant. Let's calculate the differences:
From x = -2 to x = -1: y increases by 4 (20 - 16 = 4)
From x = -1 to x = 0: y increases by 4 (24 - 20 = 4)
From x = 0 to x = 1: y increases by 4 (28 - 24 = 4)
From x = 1 to x = 2: y increases by 4 (32 - 28 = 4)
As we can see, the differences between consecutive y-values are always 4.
Since the differences between consecutive y-values are constant, the table represents a linear function. Thus, the correct answer is A: Linear.
Linear means there is a 1 to 1 correspondence.
Linear also means that if you were to graph it, it would be a straight line : )
note that at each step, x changes by the same amount: 1
Since y also changes by the same amount at each step, the function is linear. Since y changes by 4 when x changes by 1, the slope of the line is 4.