Question

What is the best way to find the domain and range of any given function? Is there a universal way to find Domain and Range?

Answer 1

For polynomials you can assume the domain is all real numbers. and the range is all real numbers if the highest exponent is odd, otherwise, probably 0 to inf or 0 to -inf (depending on the signs)

for trig functions, you have to learn the range of sin, cos are -1 to 1

for functions that have roots, you exclude negative numbers from the domain

for functions with division, exclude anything from the domain that causes divide by 0