Domain and range - Exploration
In the app below, select the property that you want to explore, then follow the instructions.
The small points on the function graph allow you to change its shape.
A matter of existence...
We know that:
- polynomials exist for any value of the variable
- fractions exist if their denominators are non-zero
- roots with an even index exist if their radicands are non-negative
- roots with an odd index exist for all values of the radicand
If the analytical expression of a function contains more "parts" that need conditions to exist, then the function exists for all values of the variable that satisfy all these conditions.
Do the functions and have the same domain? Explain your conjecture, than calculate the domain(s) of and .
What is the domain of ? And the range?