Question

I would like some help please!!
Determine which function has the greatest rate of change as x approaches infinity.
A. f(x) = 2x − 10
B.g(x) = 16x − 4
C.h(x) = 3x^2 − 7x + 8
D.There is not enough information to determine the answer.

Answer 1

Answer:

(C).

Step-by-step explanation:

Rate of change = (change in y) / (change in x)

(A). Rate of change = m = 2

(B). Rate of change = m = 16

(C). Function is not linear and range of change is not constant. So, we have to calculate average rate of change, which is slope of secant line.

If $x_{1}$ = 2 , then h(2) = 6

If $x_{2}$ = 20 , then h(4) = 1068  

(1068 - 6) / (20 - 2) ≈ 59

Thus, average rate of change of h(x) is the greatest.