# Function Family Builder

- Author:
- Judah L Schwartz

This environment allows you to explore families of linear, quadratic and absolute value functions.
Can you make any linear function with this environment?
Can you make any quadratic function with this environment?
Can you make any absolute value functions with this environment?
For the cases examined in this environment
•Vertical sliding of f(x) leads to f(x) + a. [Which way does the function slide if a>0? a<0?]
•Horizontal sliding of f(x) leads to f(x+a). [Which way does the function slide if a>0? a<0?]
•Vertical stretching & squeezing of f(x) leads to af(x). [What happens to the function if a<0? 0<a<1? a>1? ]
•Horizontal stretching & squeezing of f(x) leads to f(x/a). [What happens to the function if a<0? 0<a<1? a>1? ]
Do you believe these statements are true for any function of one variable? If so, can you prove it? If not, can you find a counterexample?