Find domain and range of y = {2}^( - x) Please Help!!​

Question

Find domain and range of y =
`{2}^( - x)`

Please Help!!​

Answer 1

The domain and range of the function y = 2^(-x) are:

Domain: All real numbers.

Range: The range of the function is (0, infinity). This means that the function takes on all positive values, but never reaches zero or negative values.

To see why, note that as x approaches positive infinity, 2^(-x) approaches zero, but never quite reaches it. Similarly, as x approaches negative infinity, 2^(-x) approaches infinity, but never quite reaches it. Therefore, the range of the function is (0, infinity).

Answer 2

Domain: (-∞, +∞)

Range: (0, +∞)

Explanation:

The domain and range of the function y = 2^{-x} can be found by using the function's definition.

Domain

The domain of a function is the set of all possible values for the independent variable (in this case, x) for which the function is defined.

In the case of y = 2^{-x}, the base of the exponentiation is 2, and any real number can be raised to a power.

Therefore, there are no restrictions on the values of x, and the domain is the set of all real numbers, (-∞, +∞).

Range

The range of a function is the set of all possible values for the dependent variable (in this case, y) that the function can take.

For the function, y = 2^(-x), the base 2 raised to any power will always be positive, except when x approaches positive infinity. As x approaches positive infinity, 2^(-x) approaches zero.

Thus, the range of the function is (0, +∞), meaning y can take any positive value but cannot be zero.

In summary:

Domain: (-∞, +∞)

Range: (0, +∞)

I hope this is helpful! Let me know if you have any other questions.