Question

From x=1 to x=2, the graph is (linear or nonlinear) and (increasing or decreasing)

Answer 1

We have here a quadratic function. In this kind of function, the rate of change is not constant (as it happens in a linear function). Then, we can say that the graph is nonlinear, that is, it does not have the same behavior as a line does.

To determine if the graph is increasing or decreasing from x = 1 to x =2, we need to calculate the rate of change for this function as follows:

We can see from the graph that:

For x = 1 ---> y = 2.

For x = 2 ---> y = -1.

Then, we have:

x1 = 1, y1 = 2

x2 = 2, y2 = -1

`m=(y_2-y_1)/(x_2-x_1)\Rightarrow m=(-1-2)/(2-1)\Rightarrow m=-(3)/(1)\Rightarrow m=-3`

Then, we can see that the function is decreasing from x = 1 to x = 2 (the rate of change is negative.)

In summary, we can say the function is nonlinear and it is decreasing from x = 1 to x =2.