Identify intervals where a function increases or decreases and compute its average rate of change over an interval.
A graph tells a story if you read it left to right. On some intervals the function is increasing (climbing as x grows), on others decreasing (falling), and the turning points in between are worth noticing. This is the same idea as slope from Algebra I, but now the "slope" is allowed to change from place to place, because most functions this year are not straight lines.
Average rate of change measures how much a function changes per unit of x between two specific points -- computed exactly like slope: (change in output)/(change in input), or (f(b) - f(a)) / (b - a). For a straight line this number is the same everywhere (that is what makes it a line). For a curve it is only true "on average" across that one interval -- it can be positive, negative, or even zero, depending on where the curve started and ended.
Mastery looks like: They compute average rate of change correctly using (f(b)-f(a))/(b-a) and can name an interval where a function is increasing or decreasing.
Common stumbles: Subtracting the endpoints in the wrong order (mismatching numerator and denominator); assuming a rate of change of 0 means the function was constant the whole interval.