Question

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).

Answer 1

Answer: D

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)