Graph the piecewisedefined function fx 4 if x SolutionAvg r

Graph the piecewise-defined function f(x) = {4, if x

Solution

Avg. rate of change is given by:

= [f(m) - f(n)]/(m - n)

here we need to find avg. rate of change from x = 1 to x = a

f(x) = 1/x

f(1) = 1/1 = 1

f(a) = 1/a

So,

Avg. rate of change = (1 - 1/a)/1 - a

= [(a - 1)/a]/(1 - a)

= (a - 1)/[-a*(a - 1)]

= -1/a