What is the domain and the range of f(x)=3x+4

The domain of a function can be restricted pretty much anyway you want. However, in this case, they are looking for the set of x values that can be put into the function without causing a division by zero or a point discontinuity. In the case of f(x) = 3x+4, there are no values of x that cause a problem so we can write the domain in interval notation as (-∞, ∞). The range follows from the domain and is also (-∞, ∞).