Final answer:
The domain of the function f(x) = (x^2 + 13x - 4)/10 is all real numbers. The range of the function is f(x) ≥ -207/20.
Step-by-step explanation:
The domain of a function represents the set of all possible input values (x-values) for the function, while the range represents the set of all possible output values (y-values) for the function. In this case, the function f(x) = (x^2 + 8x + 5x - 4)/10 simplifies to f(x) = (x^2 + 13x - 4)/10.
To find the domain, we need to determine the values of x that will result in a valid output for f(x). Since the function is a quadratic equation, it will have a valid output for all real numbers. Therefore, the domain is all real numbers.
To find the range, we need to determine the possible values of f(x) for the given domain. Since the leading coefficient of the quadratic equation is positive, the graph of the function opens upward, indicating that the range is greater than or equal to the minimum value of f(x). The minimum value occurs at the vertex of the parabola, which can be found using the formula x = -b/2a. Plugging in the coefficients from the equation, we get x = -13/2. Substituting this value back into the equation, we get f(x) = -207/20.
Therefore, the range of the function is f(x) ≥ -207/20.