The function f(x) = 26x^3 is a cubic polynomial function. To determine the range of a polynomial function, we first analyze the behavior of the function as x approaches positive and negative infinity.
As x approaches positive infinity (x → +∞), the term 26x^3 will also approach positive infinity (f(x) → +∞). Conversely, as x approaches negative infinity (x → -∞), the function will approach negative infinity (f(x) → -∞). This indicates that the cubic function will cover all real numbers.
Therefore, the range of the function f(x) = 26x^3 is all real numbers, which can be expressed in interval notation as:
Range: (-∞, +∞)
In conclusion, the cubic nature of the function allows it to take on all possible y-values, confirming that the range is indeed all real numbers.