Question

The temperature was recorded at several times during the day. Function T gives the temperature in degrees Fahrenheit, n hours since midnight. Here is a graph for this function.

Drag and drop to indicate whether the average rate of change is positive, negative, or zero for each interval.



From n=1 to n=5 Response area

From n=5 to n=7 Response area

From n=10 to n=20 Response area

From n=15 to n=18 Response area

From n=20 to n=24 Response area

Answer 1

The answers are as follows n=5 to n=7 | Negative; n=10 to n=20 Positive n=15 to n=18 | Zero; n=20 to n=24 | Negative

The average rate of change of a function is the slope of the secant line that intersects the graph of the function at the two endpoints of the interval. If the slope is positive, then the function is increasing over the interval. If the slope is negative, then the function is decreasing over the interval. If the slope is zero, then the function is constant over the interval.

From n=1 to n=5:

The secant line has a positive slope, so the average rate of change is positive. This means that the temperature is increasing over this interval.

From n=5 to n=7:

The secant line has a negative slope, so the average rate of change is negative. This means that the temperature is decreasing over this interval.

From n=10 to n=20:

The secant line has a positive slope, so the average rate of change is positive. This means that the temperature is increasing over this interval.

From n=15 to n=18:

The secant line is horizontal, so the average rate of change is zero. This means that the temperature is constant over this interval.

From n=20 to n=24:

The secant line has a negative slope, so the average rate of change is negative. This means that the temperature is decreasing over this interval.