### Instruction: Find the range of the function
\[j(x) = \frac{5x + 3}{x}.\].### Response: To find the range of a function, I need to consider what values it can output for different inputs in its domain.
The domain of this function is all real numbers except x = 0, since dividing by zero is undefined.
I can rewrite the function as
\[j(x) = \frac{5x}{x} + \frac{3}{x} = 5 + \frac{3}{x}.\]
This makes it easier to see how the function behaves as x approaches different values.
As x gets very large or very small, the fraction 3/x gets closer to zero, so the function approaches 5.
As x gets closer to zero from the positive side, the fraction 3/x gets larger and larger, so the function increases without bound.
As x gets closer to zero from the negative side, the fraction 3/x gets more and more negative, so the function decreases without bound.
This means that the function has no maximum or minimum value, but it has a horizontal asymptote at y = 5.
Therefore, the range of the function is all real numbers except 5, or in interval notation, (-infinity, 5) U (5, infinity).