The function f(x) = 2x^3 + 3x^2 - x + 5 is a polynomial of degree 3, meaning its highest exponent is 3. This type of function can have up to three real roots, which are the values of x where f(x) = 0 . The leading coefficient is 2, indicating that as x approaches positive or negative infinity, the function will rise towards positive infinity. The graph of this function will have a characteristic "S" shape, typical of cubic functions. It may have one or two turning points, where the function changes direction. The constant term, 5, indicates that when x = 0 , the value of f(x) is 5, which is the y-intercept on the graph.