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
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-2}{2-1}\Rightarrow m=-\frac{3}{1}\Rightarrow m=-3[/tex]
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.
