Consider the functions shown below. determine which of the following statements is true. a. as the value of x decreases, both the values of f(x) and g(x) will eventually be negative. b. at x = -1, f(x) = g(x). c. for x ≤ 1, g(x) < f(x). d. as the value of x increases, the value of g(x) will eventually exceed the value of f(x).

D

Step-by-step explanation:

A. False

f(x): x → -∞, y → -∞

g(x): x → -∞, y → 1  

B. False

at x = -1, f(x) = -7

at x = -1, g(x) = 1.5

C. False

refer to A

g(x) → 1 and f(x) → -∞   so g(x) > f(x)

D. TRUE

It is hard to tell from the graph so plug in a value to check.

f(10) = 5(10) - 2

       = 50 - 2

       = 48

g(10) = 2¹⁰ + 1

        = 1024 + 1

        = 1025

g(10) > f(10)