Question

PLEASE HELP NEED HELP ASAP:Which of these statements is true for f(x)=(1/2)^x

OO
OA. The domain of f(x) is x > 0.
B. It is always increasing.
O C. The range of f(x) is y> 1/2.
OD. The y-intercept is (0, 1).
?

Answer 1

The domain of f(x) is x > 0.

Step-by-step explanation:

To determine which of the statements is true for the function f(x) = (1/2)^x, let's analyze each option:

OA. The domain of f(x) is x > 0. This statement is true because the function is defined for all values of x greater than 0.

B. It is always increasing. This statement is false as the function is actually decreasing as x increases. As x gets larger, the fraction (1/2)^x becomes smaller.

O C. The range of f(x) is y > 1/2. This statement is false as the range of the function is actually the set of positive real numbers between 0 and 1, not including 1/2.

OD. The y-intercept is (0, 1). This statement is false as the y-intercept of the function is (0, 1/2). The y-coordinate corresponds to the value of the function when x is 0.

Therefore, the statement OA. The domain of f(x) is x > 0. is the only true statement.