Question

Consider the two functions f(x) and g(x), where f(x) = 2x and g(x) is graphed below.

Answer 1

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.