Identify the domain, range and asymptotes of f(x) = 5x+3 +10.

The function given is f(x) = 5x + 3 + 10, which simplifies to f(x) = 5x + 13.

1. Domain: The domain of a function is the set of all possible input values (often 'x' values) which will output real numbers. Since there are no restrictions on 'x' in this function (there are no denominators that 'x' could make zero, no even roots of negative numbers, etc.), the domain of this function is all real numbers. In interval notation, this is (-∞, ∞).

2. Range: The range of a function is the set of all possible output values (often 'f(x)' or 'y' values). Since this is a linear function and there are no restrictions on the output, the range is also all real numbers, or (-∞, ∞).

3. Asymptotes: Asymptotes are lines that a graph approaches but never touches. For this linear function, there are no asymptotes because the graph of the function does not approach a line without touching it. The graph of this function is a straight line, so it doesn't have any asymptotes.