What is the domain and range of g(x) = (1/3) to the power of x?
The domain is all real numbers (- infinity to infinity)
The range is zero to infinity
To find the domain of a function, you need to determine which values of x are acceptable inputs for the function. In this case, since the function is defined as g(x) = (1/3)^x, any real number can be raised to a power, so there are no restrictions on the values of x. Therefore, the domain of g(x) is all real numbers, or (-∞, ∞).
To find the range of a function, you need to determine the set of all possible output values of the function. In this case, as x approaches positive infinity, (1/3)^x approaches zero, but it never actually reaches zero. Similarly, as x approaches negative infinity, (1/3)^x approaches infinity, but it never actually reaches infinity. Therefore, the range of g(x) is from zero (inclusive) to infinity (exclusive), or [0, ∞).