The word translation in mathematics does not mean to change the language of something, but there is maybe some similarity in the meaning. When we translate a shape, we change its position (i.e. we move it) but without changing its size, shape or rotating it.

In this chapter, we will learn about how to translate the graph, $y=f(x)$, of a function $f$ by changing the expression for $f.$ We will see this same idea many times in the rest of the course, so let's get going and learn all about it!

1. Complete the tables below:

   $$\begin{array}{rcccccc}x& 0& 1& 2& 3& 4& 5\\ x^2& & & & & & \\ (x+1{)}^2& & & & & & \end{array}$$$$\begin{array}{rcccccc}x& -2& -1& 0& 1& 2& 3\\ x^2& & & & & & \\ x^2+1& & & & & & \end{array}$$

   Sketch each curve. What do you notice?

2. Let $f(x)=x^3.$

   Sketch the curves

   $$y=f(x+3)-2\text{ and }y=f(x-1)+3$$