Linear Translations

Author:
Victoria
Topic:
Algebra, Geometric Transformations, Translation
Function Transformations: Exploring Vertical and Horizontal Shifts of a Linear Function
Round 1 Shift your function right, any number of units (without moving up or down), and then record the new values for the x- and y-coordinates of the plotted points for your given function. Compare the new ordered pairs to the values of the original function -
  • How many units to the right did you shift the function? __________
  • Which values changed, the x- or y-coordinates? How? _____________________________________________
Round 2 Return your given function to your initial starting point. Shift your function left, any number of units (without moving up or down), and then record the new values for the x- and y-coordinates of the plotted points for your given function. Compare the new ordered pairs to the values of the original function -
  • How many units to the left did you shift the function? __________
  • Which values changed, the x- or y-coordinates? How? _____________________________________________
Rounds 1 & 2 Whenever a function is “shifted” left or right, this type of translation is known as a horizontal shift. Can you write a “rule” to describe how your values changed when you shifted the function?
  • Shifting the function right - ____________
  • Shifting the function left - ____________
Round 3 Return your given function to your initial starting point. Shift your function up, any number of units (without moving left or right), and then record the new values for the x- and y-coordinates of the plotted points for your given function. Compare the new ordered pairs to the values of the original function -
  • How many units up did you shift the function? __________
  • Which values changed, the x- or y-coordinates? How? _____________________________________________
Round 4 Return your given function to your initial starting point. Shift your function down, any number of units (without moving left or right), and then record the new values for the x- and y-coordinates of the plotted points for your given function. Compare the new ordered pairs to the values of the original function -
  • How many units down did you shift the function? __________
  • Which values changed, the x- or y-coordinates? How? _____________________________________________
Rounds 3 & 4 Whenever a function is “shifted” up or down, this type of translation is known as a vertical shift. Can you write a “rule” to describe how your values changed when you shifted the function?
  • Shifting the function up - ____________
  • Shifting the function down - ____________
Round 5 Return your given function to your initial starting point. Shift your function right or left any number of units and up or down any number of units, then record the new values for the x- and y-coordinates of the plotted points for your given function. Compare the new ordered pairs to the values of the original function -
  • How many units to the right or left (circle one) did you shift the function? __________
  • How many units to the up or down (circle one) did you shift the function? __________
  • What happens to the value of the x-coordinates? _____________________________________________
  • What happens to the value of the y-coordinates? _____________________________________________
Wrap It UP! Let all x-coordinate values be represented by x, and let all y-coordinate values be represented by f(x). Write a general rule for the following translations that can be performed on any function in the coordinate plane.
  • A horizontal shift of m units on a function, results in the following function notation - ___________________
  • A vertical shift of n units on a function, results in the following function notation - ___________________
  • A horizontal shift of m units and a vertical shift of n units, results in the following - ___________________