Question

Tell whether the function shown by the table is linear or nonlinear.

x:10.5,2,17,4.5
y:5,23.5,30,36.5
​

a) Linear
b) Nonlinear

Answer 1

The function represented by the table is nonlinear, as the rates of change between the x-values and y-values are not constant. the given function is nonlinear.

Step-by-step explanation:

To determine if a function represented by a table is linear or nonlinear, we can check if there's a constant rate of change between the x-values and the corresponding y-values. For linear functions, the rate of change (or the slope) is consistent. In the table with points (1,5), (2,10), (3,7), and (4,14), we can calculate the differences between successive y-values and corresponding x-values to see if the slope is constant.

• From (1,5) to (2,10), the change in y is 5 and the change in x is 1, giving us a slope of 5/1 or 5.
• From (2,10) to (3,7), the change in y is -3 and the change in x is 1, giving us a slope of -3/1 or -3.
• From (3,7) to (4,14), the change in y is 7 and the change in x is 1, giving us a slope of 7/1 or 7.

Since the slope is not consistent across all intervals (it changes from 5 to -3 to 7), the function is nonlinear. We can infer this from the dependence of y on x which does not follow a constant rate of change as it would in a linear function. Thus, the given function is nonlinear.