Question

Find domain and range of the function y=3(1/5)^x

Show your work.

A)D=(All real numbers), R= {y|y<0)
B)D=(all real numbers), R= {y|y>0)
C)D=y, R=x
D) x , {all real numbers}

Answer 1

Answer: B) D=(all real numbers), R= y

Explanation:
To find the domain and range of the function y = 3(1/5)^x, we need to analyze the behavior of the function.

Domain:

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. Since the function y = 3(1/5)^x involves an exponential expression, it is defined for all real numbers. There are no restrictions on the values of x that can be input into the function. Therefore, the domain is all real numbers.

Range:

The range of a function refers to the set of all possible output values (y-values) that the function can produce. In the case of the function y = 3(1/5)^x, we have a positive exponential decay function. This means that as x increases, the function's value (y) approaches zero, but it never actually reaches zero. Moreover, since the base (1/5) and the coefficient (3) are both positive, the function will always produce positive y-values. Therefore, the range is all positive real numbers, or y > 0.