Exploring the Function f(x) = x³ | Domain, Range, Graph, Zeroes, and More

f(x) = x³

The function f(x) = x³ is a polynomial function

The function f(x) = x³ is a polynomial function. The term x³ represents x raised to the power of 3, which means that any value of x is cubed.

To understand this function better, let’s break it down:

1. Domain: The domain of a function refers to the set of all possible input values or x-values. For the function f(x) = x³, the domain is all real numbers. This means that you can substitute any real number for x in the function.

2. Range: The range of a function refers to the set of all possible output values or y-values. For the function f(x) = x³, the range is also all real numbers. This means that the function can produce any real number as an output.

3. Graph: To visualize the function, we can plot it on a graph. The graph of f(x) = x³ is a curve that passes through the origin (0, 0). As x increases, the function also increases. The graph is symmetrical about the y-axis since the function is an odd function.

4. Zeroes or x-intercepts: The zeroes or x-intercepts of a function are the values of x for which the function equals zero. For the function f(x) = x³, the only zero is x = 0. This means that the graph intersects the x-axis at the point (0, 0).

5. Increasing and decreasing intervals: The function f(x) = x³ is always increasing. As x gets larger or smaller, the function value also increases. There are no decreasing intervals for this function.

6. Sign: The sign of a function refers to whether the function value is positive, negative, or zero. For the function f(x) = x³, the sign depends on the sign of the input value. If x is positive, then f(x) is positive. If x is negative, then f(x) is negative. And if x equals zero, then f(x) is zero.

7. Behavior at infinity: As x approaches positive or negative infinity, the function f(x) = x³ also approaches positive or negative infinity, respectively. This means that the graph of the function has no horizontal asymptote.

I hope this explanation helps you understand the function f(x) = x³ better! If you have any further questions, feel free to ask.

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