Q:

Consider the two functions f(x) and g(x), where f(x) = 2x and g(x) is graphed below.Graph of g(x)Compare the rate of change of the two functions on the interval 2 ≤ x ≤ 3.The rate of change of the function g(x) is greater than f(x).The rate of change of the function f(x) is greater than g(x).The rate of change of the function f(x) and g(x) are the same.

Accepted Solution

A:
The function g (x) is:
 y-yo = m (x-xo)
 m = (y2-y1) / (x2-x1)
 m = (4-2) / (2-1)
 m = (2) / (1)
 m = 2
 We choose an ordered pair:
 (xo, yo) = (0, 0)
 Substituting values:
 y-0 = 2 (x-0)
 Rewriting:
 y = 2x
 g (x) = 2x
 The rate of change of both functions is the same and is given by the slope of the line:
 m = 2
 Answer:
 The rate of change of the function f (x) and g (x) are the same.