Determine whether the following function is proper or improper: \(f(x) = \frac{4x^2 + 5x + 2}{2x^2 + 3x + 1}\)
Answer
Step 3: Since the degree of the numerator is equal to the degree of the denominator, the function is improper.
Step 1 ：Step 1: A rational function \(\frac{P(x)}{Q(x)}\) is said to be proper if the degree of the polynomial in the numerator \(P(x)\) is less than the degree of the polynomial in the denominator \(Q(x)\). Otherwise, it is said to be improper.
Step 2 ：Step 2: In the given function \(f(x) = \frac{4x^2 + 5x + 2}{2x^2 + 3x + 1}\), the degree of the polynomial in the numerator is 2 and the degree of the polynomial in the denominator is also 2.
Step 3 ：Step 3: Since the degree of the numerator is equal to the degree of the denominator, the function is improper.
