Final answer:
The domain of the function f(x) = -2x^2 + 10x + 2 is all real numbers. The range of the function is (-∞, 15].
Step-by-step explanation:
The domain of a function represents the set of all possible input values, or x-values, for the function. In this case, since the function is a quadratic equation, there are no restrictions on the input values. Therefore, the domain of the function f(x) = -2x^2 + 10x + 2 is all real numbers.
The range of a function represents the set of all possible output values, or y-values, for the function. Since the function is a downward-opening quadratic equation, the range will have an upper bound.
To find the range, we can determine the vertex of the parabola by using the formula x = -b/2a. In this case, a = -2 and b = 10. Plugging these values into the formula, we get x = -10/(-4) = 5/2 = 2.5.
Substituting this value back into the original equation, we get f(2.5) = -2(2.5)^2 + 10(2.5) + 2 = 15. Therefore, the range of the function is (-∞, 15].