Answer:
Range of y = 2^x is all positive real numbers.
Range of the function y = 2^{-x} is all positive real numbers excluding zero
Explanation:
Find the range of y = 2^x
Answer:
- Since 2^x is an exponential function with a base of 2, the function will always output positive values.
This means that the range of y is all positive real numbers, or y > 0.
In mathematical notation, we can express the range as:
Therefore, the range of y = 2^x is all positive real numbers .

Find the range of y = 2^(-x)
Answer:
Since 2^{-x} represents the reciprocal of 2^x, the function will output positive values as the exponent becomes more negative.
- As x approaches positive infinity
, the value of 2^{-x} approaches 0. - As x approaches negative infinity
, the value of 2^{-x} approaches positive infinity.
Therefore, the range of the function y = 2^{-x} is all positive real numbers greater than zero, but does not include zero itself.
In mathematical notation, we can express the range as:

Therefore, range of the function y = 2^{-x} is all positive real numbers excluding zero.