Answer
a) Linear function
b) Quadratic function
c) Rational function
d) Square root function
Work Step by Step
Okay, let me explain the characteristics of a quadratic function in more detail.
A quadratic function is a polynomial function of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers, and a ≠ 0.
The key features of a quadratic function are:
1. It has a degree of 2, meaning the highest exponent of the variable x is 2.
2. The graph of a quadratic function is a parabola, which is a U-shaped curve.
3. The coefficient "a" determines the orientation of the parabola. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward.
Now, let's analyze the options in the question:
a) f(x) = 3x + 2 - This is a linear function, not a quadratic function, as it does not have an x^2 term.
b) f(x) = 2x^2 + 3x - 1 - This is a quadratic function, as it is in the form f(x) = ax^2 + bx + c, where a = 2, b = 3, and c = -1.
c) f(x) = 4/x - This is a rational function, not a quadratic function, as it does not have the form of a quadratic polynomial.
d) f(x) = √(x - 1) - This is a square root function, not a quadratic function, as it does not have the form of a quadratic polynomial.
Therefore, the correct answer is option b) f(x) = 2x^2 + 3x - 1, as it is the only function that meets the criteria of a quadratic function.
