Cubic Parent Function
x →∞, f(x) →∞x → -∞, f(x) → -∞
The cubic parent function is a type of polynomial function that takes the form f(x) = x³. It is a third-degree polynomial function that has a graph that is symmetric about the origin.
There are a few characteristics of the cubic parent function that are important to note:
1. Domain and range: The domain and range of the cubic function are all real numbers. This means that any value of x can be plugged into the function and any value of y can be produced.
2. Zeros: The cubic parent function has one zero at the origin. This means that if x = 0, the value of the function will also be 0.
3. Increasing and decreasing intervals: The cubic function is increasing for all values of x greater than 0, and decreasing for all values of x less than 0.
4. End behavior: The end behavior of the cubic function is the same as the end behavior of any odd-degree polynomial function. As x approaches negative or positive infinity, the function approaches negative or positive infinity, respectively.
5. X-intercepts and y-intercept: The cubic function has one x-intercept at the origin, and the y-intercept is also at the origin.
6. Symmetry: The cubic function is symmetric about the origin. This means that for any point (x, y) on the graph, (-x, -y) is also on the graph.
Overall, the cubic parent function is a fundamental function in algebra that has many important properties and applications. It is used in a wide range of real-world scenarios, from physics to economics to computer graphics.
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