# Horizontal Translation

- Author:
- Guillermo Bautista

- Topic:
- Functions, Quadratic Functions, Translation

Shown below is the graph of the function

**f(x) = x**. Graph the functions^{2}**u(x) = (x - 3)**and then^{2}**v(x) = (x + 5)**by typing their equations in the Input bar.^{2}## Questions to think about

1.) What are your observations about the graphs of

*f*,*u*, and*v*? 2.) How does adding a number to the input of a function affect its graph? 3.) How does subtracting a number from the input of a function affect its graph? 4.) What conjectures can you make based on your answers above?## TIP

Since

**f(x) = x**, another way to graph^{2}**u(x) = (x - 3)**is to type^{2}**u(x) = f(x - 3)****.**