Question

Calculate the average rate of change of the function f(x) over the interval -[4,-1] using the formula. A_____ The value of f(-1) is.B._____The value of f(-4) is. C.________ the average rate of change of f(x) over the interval [-4,-1] is D.________
GRAPH WITH QUESTION: Y intercept:5 X intercept: -2.5 slope: 2

A: [f(-4)-f(-1)]/[-5]
[f(-1)-f(-4)]/[-5]
[f(-1)-f(-4)]/[3]
[f(-4)-f(-1)]/[3]
B. 3
2
-1
C. -4
-3
4
D. -2
-1.5
2
4

Answer 1

First we write the equation of the line in its standard form:
 y-yo = m (x-xo)
 Where:
 m = 2
 We choose an ordered pair:
 (xo, yo) = (0, 5)
 Substituting the values:
 y-5 = 2 (x-0)
 Rewriting:
 y = 2x + 5

 Part A:
 The average rate of change of the function f (x) over the interval [-4, -1] using the formula:
 [f (-1) -f (-4)] / [3]
 Part B:
 The value of f (-1) is:
 y = 2 (-1) +5
 y = 3
 Part C:
 The value of f (-4) is:
 y = 2 (-4) +5
 y = -3
 Part D:
 the average rate of change of f (x) over the interval [-4, -1] is
 m = [f (-1) -f (-4)] / [3]
 m = (3 - (- 3)) / 3
 m = (3 + 3) / (3)
 m = 6/3
 m = 2