Answer:
[tex] = -\frac{1}{3} [/tex]
Step-by-step explanation:
Given:
[tex] f(x) = \frac{4x - 6}{x} [/tex]
Required:
Average range of change over [-3, 6]
SOLUTION:
Find f(-3) and f(6):
To find f(-3), replace x with -3 in the given function
[tex] f(-3) = \frac{4(-3) - 6}{-3} [/tex]
[tex] f(-3) = \frac{-12 - 6}{-3} [/tex]
[tex] f(-3) = \frac{-18}{-3} [/tex]
[tex] f(-3) = 6 [/tex]
To find f(6), replace x with 6 in the given function
[tex] f(6) = \frac{4(6) - 6}{6} [/tex]
[tex] f(6) = \frac{24 - 6}{6} [/tex]
[tex] f(6) = \frac{18}{6} [/tex]
[tex] f(6) = 3 [/tex]
Average rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
[tex] a = -3, f(a) = 6 [/tex]
[tex] b = 6, f(b) = 3 [/tex]
Plug in the values into the formula for average rate of change.
[tex] = \frac{3 - 6}{6 -(-3)} [/tex]
[tex] = \frac{-3}{9} [/tex]
[tex] = \frac{-1}{3} [/tex]
Average rate of change [tex] = -\frac{1}{3} [/tex]
