2C-1. Combining Functions with Operations
Instructions:
- Use the input boxes for and to define the two functions you want to combine.
- Adjust the slider tools for and to stretch/shrink or reflect the graphs of and individually.
- Use the slider tool "Combine f and g" to change the operation used to combine and to define a new function . There are four options: addition, subtraction, multiplication, and division.
Combining Functions
Many real world relationships are too complex to describe with a single function formula. Two (or more) functions can be combined through the usual arithmetic operations (addition, subtraction, multiplication, division) to create new functions with their own behavior that can better model a real world relationship.
The new function is created by combining the outputs of two (or more) functions through the usual arithmetic operations. For example:
- Addition:
- Subtraction:
- Multiplication:
- Division: , where .
- Constant Multiple: for some constant .