Question

Is the function in the table linear or nonlinear and why? x y 0,−100 and 1,-50 and 2,0 and 3,100 and 4,150. (A)The function is not linear because there are negative values in the y values. (b) The function is linear because the y values are multiples of 50. (c) The function is not linear because the rate of change is not constant. (D) The function is linear because the x values increase by a constant number.

Answer 1

The function in the table is not linear because the rate of change of y-values for each unit increase in x is not constant, showing a non-linear relationship.

Step-by-step explanation:

To determine if a function is linear or nonlinear, we need to look at the rate of change of the y-values relative to the x-values. A linear function has a constant rate of change, which means that for equal increments in x, the change in y should also be constant.

Let's analyze the given data:
(0,-100), (1,-50), (2,0), (3,100), and (4,150). If we calculate the changes in y for each unit increase in x, from -100 to -50 there is a change of +50, from -50 to 0 there is a change of +50, but from 0 to 100 there is a change of +100, and finally, from 100 to 150 there is a change of +50. The changes in y are not consistent; the rate of change is not constant. Therefore, the correct answer is (C) The function is not linear because the rate of change is not constant.

Answer 2

The correct option is c.

Step-by-step explanation:

Linear function: The rate of change of a linear function is always constant.

Non-Linear function: The rate of change of a non-linear function is not constant.

From the given coordinate pairs it is noticed that the function is passing through the points (0,-100), (1,-50), (2,0), (3,100) and (4,150).

`m=(y_2-y_1)/(x_2-x_1)`

The slope of function for points (0,-100) and (1,-50) is

`m_1=(-50-(-100))/(1-0)=50`

The slope of function for points (2,0) and (3,100) is

`m_2=(100-0)/(3-2)=100`

Since the slopes of function are different, therefore the given function is non-linear.

The function is not linear because the rate of change is not constant and option c is correct.