Question

The function f(x) is graphed below. In two or more complete sentences, describe how to find the interval(s) where the function is decreasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is decreasing.

Answer 1

The function is decreasing from the x values of -8 to 5 and again from 4 to 8. In interval notation this would be [-8,5)U[4,8). (You can tell that the function is decreasing because it has a negative slope or it is going downwards).

Answer 2

The function is decreasing in the interval [-8,-5) and [4,8).

Explanation:

The graph of function is a straight line such that in the interval [-8,-5) we get a function as a straight line with negative slope and in the interval [-5,0] the function is a straight line with zero slope ( since the line is horizontal and parallel to x-axis) and in the interval [0,4] the function is a straight line with positive slope and in the interval [4,8) the function is a straight line with negative slope.

We know that a function is decreasing if the slope of function at each point is negative.

and if the function is increasing then the slope of function is positive and function is constant then slope is zero.