Understanding vertical and horizontal translations is important when you are graphing functions. Let’s break these concepts down into simpler terms.

Vertical Translations:

• What It Is: A vertical translation moves the graph either up or down.

• How It Works: It is shown by (f(x) + k), where (k) is a number.

  • If (k) is a positive number (greater than 0), the graph moves up.

  • If (k) is a negative number (less than 0), the graph moves down.

• Example: Take the function (f(x) = x^2). If we shift it up by 3, we get (f(x) = x^2 + 3).

Horizontal Translations:

• What It Is: A horizontal translation moves the graph either left or right.

• How It Works: It's shown by (f(x - h)), where (h) is a number.

  • If (h) is a positive number (greater than 0), the graph moves to the right.

  • If (h) is a negative number (less than 0), the graph moves to the left.

• Example: For the function (f(x) = x^2), if we shift it to the right by 2, we get (f(x) = (x - 2)^2).

These translations help us understand how to change the position of graphs on a coordinate plane.