Final answer:
The domain of the function y=log₂(8+5x) is x > -8/5 and its range is all real numbers, since logarithmic functions can produce any real number as output.
Step-by-step explanation:
The student is asking to find the domain and range of a logarithmic function, specifically y = log₂(8+5x). When determining the domain of logarithmic functions, one must remember that the argument must be greater than zero. Thus, for the equation 8 + 5x > 0, we find that x must be greater than -8/5. Therefore, the domain of the function is all real numbers x such that x > -8/5.
As for the range of logarithmic functions, it is all real numbers because the output of a logarithm can take on any real value. As x approaches infinity, y will also grow without bounds, following the pattern that as x increases, log(x) increases. Hence, no upper or lower bounds restrict the output values of y.