### Instruction: What is the domain of the function $g(x) = \frac{3x+1}{x+8}$ ?  Enter your answer using interval notation.### Response: To find the domain of a function, I need to think about what values of x make the function undefined or invalid.
In this case, the function is a rational expression, which means it has a fraction.
The only thing that can make a fraction undefined is if the denominator is zero, because we cannot divide by zero.
So I need to find what value of x makes x+8 equal to zero.
I can do that by subtracting 8 from both sides of the equation x+8 = 0, and get x = -8.
This means that x = -8 is the only value that is not in the domain of g, because it makes the function undefined.
All other values of x are allowed, so the domain is everything except x = -8.
To write this using interval notation, I need to use parentheses to exclude the value -8, and use infinity symbols to indicate that the domain extends in both directions without bound.