Questions: What is the range of the function (f(x)=3x^3) ? (Enter (r) for all Real numbers.)

Solution Steps

The given function is \( f(x) = 3x^3 \). This is a cubic function, which is a type of polynomial function.

Cubic functions have the general form \( ax^3 + bx^2 + cx + d \). The leading term \( ax^3 \) determines the end behavior of the function. Since the coefficient of \( x^3 \) is positive (3 in this case), as \( x \to \infty \), \( f(x) \to \infty \), and as \( x \to -\infty \), \( f(x) \to -\infty \).

Cubic functions are continuous and have no restrictions on their domain. They can take any real value as \( x \) varies over all real numbers. Therefore, the range of the function \( f(x) = 3x^3 \) is all real numbers.

Final Answer