Question

a table representing a continuous unrestricted exponential function is shown.

x	0	1	2	3

is the function f(x) increasing or decreasing? is it positive or negative?

• it is decreasing and negative.
• it is decreasing and positive.
• it is increasing and negative.
• it is increasing and positive.

Explanation:

To determine if the function is increasing or decreasing, we analyze the values of \( f(x) \) as \( x \) increases. When \( x = 0 \), \( f(x)=2 \); at \( x = 1 \), \( f(x)=0.5 \); at \( x = 2 \), \( f(x)=0.125 \); and at \( x = 3 \), \( f(x)=0.03125 \). As \( x \) increases from 0 to 3, the values of \( f(x) \) are getting smaller (2 > 0.5 > 0.125 > 0.03125), so the function is decreasing. To determine if it's positive or negative, we check the values of \( f(x) \): 2, 0.5, 0.125, and 0.03125 are all greater than 0, so the function is positive.

Answer:

B. It is decreasing and positive