Question

Find the range of f(x)=(1/2) x^4 + 3x − 2

Answer 1

The range is the set of y-values for a function.
Since your function doesn't seem to have any restriction it will go from -ve infinity to +ve infinity. BUT we know that a quadratic or a quartic functions has a range from the y-value of its vertex to +ve infinity (depending on the leading coefficient of the function).