Question

What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

Answer 1

Average rate of change is just the slope between the 2 points
we can do this the long way or the smart way


long way, find the 2 points and find the slope between them
when x=-5, f(-5)=-2(-5)+1=10+1=11
when x=1, f(1)=-2(1)+1=-2+1=-1
so the points are (-5,11) and (1,-1)
the slope between them is (-1-11)/(1-(-5))=(-12)/(1+5)=-12/6=-2
the answer is B, -2

smart way
recognize that that is a linear equation and the slope between any 2 points will be the m in y=mx+b
f(x)=-2x+1
the slope is -2
the average rate of change is -2
answer is B. -2

Answer 2

Answer: -2

Step-by-step explanation: