Question

Is this function linear, quadratic, or exponential?

x y
3 0.2
4
–
1.8
5
–
3.8
6
–
5.8
7
–
7.8

Answer 1

Based on the provided dataset, where the change in y is constant as x increases, the function is linear. As the difference in y-values is consistently -2 for each increase of 1 in x, it follows the pattern of a linear function.

Step-by-step explanation:

The student is asking whether the given function, based on the values of x and y provided, is linear, quadratic, or exponential. To determine the type of function, we need to analyze the pattern in the change of y values relative to x. A linear function has a constant rate of change, which means the difference between successive y-values (the slope) will be the same. A quadratic function has a rate of change that itself changes at a constant rate, so the differences between successive y-differences would be constant. An exponential function grows (or shrinks) by a constant factor, not a constant addition.

Looking at the data provided:

• From (3, 0.2) to (4, -1.8), the change in y is -2.
• From (4, -1.8) to (5, -3.8), the change in y is -2.
• From (5, -3.8) to (6, -5.8), the change in y is -2.
• From (6, -5.8) to (7, -7.8), the change in y is -2.

Since the change in y is constant (-2) as x increases by 1, this pattern is characteristic of a linear function of the form y = mx + b.