(b) Determine the domain and the range of the function The domain of \( f \) is

the set of all real numbers, since the function is defined for all real numbers. Therefore, the domain of \( f \) is \( (-\infty, \infty) \). To find the range of \( f \), we need to consider the possible values of \( f(x) \) for all \( x \) in the domain. Since \( f(x) \) is a polynomial function, it is continuous and differentiable for all real numbers. The leading coefficient of \( f(x) \) is positive, which means that the function is increasing without bound as \( x \) approaches positive infinity and decreasing without bound as \( x \) approaches negative infinity. Therefore, the range of \( f \) is also \( (-\infty, \infty) \). So, the domain and range of the function \( f \) are both \( (-\infty, \infty) \). (b) Determine the domain and the range of the function To determine the domain and range of the function, we need to consider the following: 1. Domain: The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of all x-values for which the function produces a real output value. 2. Range: The range of a function is the set of all possible output values (y-values) that the function can produce for the given domain. Let's analyze the given function: Since the function is not explicitly defined in the problem statement, we will assume it is a polynomial function, as the previous solution suggests. A polynomial function is defined for all real numbers, so the domain of the function is \( (-\infty, \infty) \). To find the range, we need to consider the behavior of the polynomial function as \( x \) approaches positive and negative infinity. Since the leading coefficient of the polynomial is positive, the function will increase without bound as \( x \) approaches positive infinity and decrease without bound as \( x \) approaches negative infinity. This means that the range of the function is also \( (-\infty, \infty) \). Therefore, the domain and range of the function are both \( (-\infty, \infty) \). If the function is not a polynomial function, please provide the explicit function definition so that we can determine the domain and range accurately.