Final answer:
The range of the function f(x)=x³+2 is (-∞, +∞).
Step-by-step explanation:
The range of the function f(x)=x³+2 can be determined by analyzing the behavior of the function as x varies. Since the highest power of x is 3, we know that the function will have a similar shape to a cubic graph. The range of the function is the set of all possible output values, or y-values, that the function can take.
To find the range, we analyze the behavior of the function as x approaches positive and negative infinity. As x approaches positive infinity, the function will also tend towards positive infinity, and as x approaches negative infinity, the function will tend towards negative infinity. Therefore, the range of the function f(x)=x³+2 is (-∞, +∞).