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"Translating Left and Right" Explained

Put parentheses around x and if it translates right put a negative sign before the number of units. If it translates left put a positive sign before the number of units.

Key Idea: Translating Left and Right

Translating a graph left or right means shifting it horizontally on the coordinate plane.

General Rule:

  • Write the equation with parentheses around :

    y=f(x±h)

  • Right translation → use a negative sign: f(x−h) moves the graph right by hh units.

  • Left translation → use a positive sign: f(x+h) moves the graph left by hh units.

Why this matters for the SAT:

Understanding horizontal translations helps you quickly recognize shifts in function graphs and match them to their equations — a common skill tested in function and graphing problems.

"Translating Up and Down" Explained

Put parentheses around y and if it translates up put a negative sign before the number of units. If it translates down put a positive sign before the number of units.

Key Idea: Translating Up and Down

Translating a graph up or down means shifting it vertically on the coordinate plane.

General Rule:

  • Write the equation as:

    y=f(x)±k

  • Upward translation → use a positive sign: f(x)+k moves the graph up by k units.

  • Downward translation → use a negative sign: f(x)−k moves the graph down by  units.

(Note: You adjust outside the parentheses, not around .)

Why this matters for the SAT:

Recognizing vertical translations helps you understand how adding or subtracting constants affects a graph’s position.
It’s key for identifying shifts in function and graphing problems.