Overview
This lesson covers the square root function ( f(x) = \sqrt{x} ), focusing on its domain and range.
Square Root Function Overview
- The square root function is defined as ( f(x) = \sqrt{x} ).
- The graph of ( f(x) = \sqrt{x} ) only exists for certain x-values.
Domain of the Square Root Function
- The domain consists of all x-values where the function is defined.
- The graph has no points for negative x; it starts at ( x = 0 ).
- The domain is all real numbers ( x \geq 0 ).
- In interval notation, the domain is ( [0, \infty) ).
Range of the Square Root Function
- The range includes all y-values that the function takes.
- There are no negative y-values; the graph starts at ( y = 0 ).
- The range is all real numbers ( y \geq 0 ).
- In interval notation, the range is ( [0, \infty) ).
Key Terms & Definitions
- Square root function — A function written as ( f(x) = \sqrt{x} ), producing non-negative results for non-negative inputs.
- Domain — The set of all possible input values (x-values) for which the function is defined.
- Range — The set of all possible output values (y-values) that the function can produce.
- Interval notation — A way of writing subsets of the real numbers; e.g., ( [0, \infty) ) means all numbers from 0 to infinity, including 0.
Action Items / Next Steps
- Practice finding domain and range for other radical (square root) functions.
- Review interval notation for use with domains and ranges.