Let's do one by one.
The domain is the set of the values of "x" a function can assume in the function and give a defined value as output.
So, the functions that don't have all real numbers as its domain are those that have some limitations, like devide by zero or square root of a negative number.
Linear:
A linear function has all real numbers as its domain, because there is no operations taht endup in undefined values.
Absolute Value:
An absolute value function is equivalent to two linear functions with restrictions. However, all "x" values can be used, because the linear functions are in a way that the limitation of one is completed by the other.
So, it has all real numbers as its domain.
Quadratic:
A quadratic equation is very similar to a linear one, but it has an extra quadratic term. However, this extra term don't have undefined vlues for "x", so it also has all real numbers as its domain.
Square Root/Radical:
This function is different, because you can't take a square root of a negative number and, in a square root function there are "x" varible inside the root, by definition. So, depending one the square root function, it doesn't have all real numbers as its domain.
Exponential:
An exponential function hax the "x" variable in an exponent of a number, when "x" is negative, the result is a fraction less than 1 and when it is positive it is a number greater than 1, but there is noo undefined values of "x". Thus, it has all real numbers as its domain.
Piecewise functions have more than one function put together to form it. Thus, its domain is dependent on the form of those function and the limits it imposes on "x", thusdepending one the piecewise function, it doesn't have all real numbers as its domain.
So, the answer to mark are:
Linear
Absolute Value
Quadratic
Exponential