Overview
This lesson covers the key properties of the cubing function ( f(x) = x^3 ), focusing on its graph, domain, and range.
The Cubing Function and Its Graph
- The cubing function is written as ( f(x) = x^3 ).
- Its graph consists of infinite points, each representing an (x, y) coordinate.
- The graph extends infinitely in both the left/down and right/up directions.
Domain of ( f(x) = x^3 )
- The domain refers to all possible x-values for which the function is defined.
- For ( f(x) = x^3 ), the graph hits every x-value from negative infinity to positive infinity.
- There are no gaps or holes in the graph along the x-axis.
- The domain is all real numbers, usually written as ( (-\infty, \infty) ).
Range of ( f(x) = x^3 )
- The range refers to all possible y-values the function can take.
- For ( f(x) = x^3 ), the graph covers all y-values from negative infinity to positive infinity.
- There are no gaps or holes in the graph along the y-axis.
- The range is all real numbers, written as ( (-\infty, \infty) ).
Key Terms & Definitions
- Domain — The set of all possible input values (x-values) for a function.
- Range — The set of all possible output values (y-values) for a function.
- Cubing Function — The function defined by ( f(x) = x^3 ).
Action Items / Next Steps
- Review the graph of ( f(x) = x^3 ) and practice identifying its domain and range.
- Be prepared to explain why both the domain and range are all real numbers.