Question

Between x = 2 and x = 3, which function has a smaller average rate of change than y = 2x ? A) y = 2 3 -x B) y = 4x - 1 C) y = 5x-2 D) y = 1 2 -x+1

Answer 1

The two points are (x, f(x)) and (x+h, f(x+h)).  To find the slope, the definition is the change in y over the change of x.  Does this sound familiar!!  Applying this definition we get the following formula:  and the points x1 = 2 and x2 = 4.  Then in our general answer, we will replace x with x1 and h = x2 - x1.  Replacing these values in the formula yields  2(2) + (4 - 2) = 4 + 2 = 6.  Thus, the slope of the secant line connecting the two points of the function is 6. Now using the same function as above, find the average rate of change between x1 = -1 and x2 = -3.  The answer is 2(-1) + ( -3 + 1) = -2 + -2 = -4.  This means that the secant line is going downhill or decreasing as you look at it from le