Transformation of Curves

Question 1

If you have a function f(x), how do you translate it?

Answer 1

To translate it by a vector of (0 a) then you should change the function to f(x) + a.
To translate it by a vector of (a 0) then you should change the function to f(x + a).

Question 2

If you have a function f(x), how do you reflect it?

Answer 2

To reflect it in the x axis, change it to -f(x).

To reflect it in the y axis then change it to f(-x).