Lesson Plan: Function Transformations: Translations Mathematics • 10th Grade

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify function transformations involving horizontal and vertical shifts.

Objectives

Students will be able to

  • understand horizontal translations of the function 𝑓(𝑥):
    • 𝑓(𝑥𝑎) corresponds to a shift of 𝑎 units in the positive 𝑥 direction,
    • 𝑓(𝑥+𝑎) corresponds to a shift of 𝑎 units in the negative 𝑥 direction,
  • understand vertical translations of the function 𝑓(𝑥):
    • 𝑓(𝑥)+𝑎 corresponds to a shift of 𝑎 units in the positive 𝑦 direction,
    • 𝑓(𝑥)𝑎 corresponds to a shift of 𝑎 units in the negative 𝑦 direction,
  • identify the resulting graph of a given graph when translated in the 𝑥-direction or 𝑦-direction,
  • sketch the graph of a given basic function when translated in the 𝑥-direction or 𝑦-direction,
  • understand how to combine a translation in the 𝑥-direction and 𝑦-direction both algebraically and graphically,
  • identify the rule of a function for which a translation in the 𝑥-direction and/or 𝑦-direction is represented graphically.

Prerequisites

Students should already be familiar with

  • function notations,
  • basic functions graphs (including simple linear, quadratic, cubic, radical, and reciprocal function graphs).

Exclusions

Students will not cover

  • function transformations involving dilation and reflection.

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