Question

Function with the same range as f(x)=−75​⋅(53​)x:

a. f(x)=−5⋅(53​)x
b. f(x)=−75​⋅(51​)x
c. f(x)=−73​⋅(35​)x
d. f(x)=−57​⋅(53​)x

Answer 1

The function with the same range as f(x) = -75⁢⋅(5/3)⁸x is f(x) = -75⁢⋅(5/1)⁸x.

Step-by-step explanation:

The function with the same range as f(x) = -75⁢⋅(5/3)⁸x is:

b. f(x) = -75⁢⋅(5/1)⁸x

To find a function with the same range as f(x), we need to find a function that has the same general shape and behavior. In this case, the function f(x) = -75⁢⋅(5/1)⁸x has a negative slope that decreases in magnitude with increasing x. Among the choices, option b, f(x) = -75⁢⋅(5/1)⁸x, stands out as it maintains a negative slope that declines in value as x increases, akin to the original function. Therefore, in terms of the general behavior and slope characteristics, option b aligns most closely with the function f(x) = -75⁢⋅(5/3)⁸x, ensuring a comparable range.