Translating Functions

Examples, solutions, and videos to help Algebra I students learn how to recognize and use parent functions for linear, absolute value, quadratic, square root, and cube root to perform vertical and horizontal translations. They identify how the graph of y = f(x) relates to the graphs of y = f(x) + k and y = f(x+k) for any specific values of k positive or negative, and find the constant value, k, given the parent functions and the translated graphs. Students write the function representing the translated graphs.

New York State Common Core Math Algebra I, Module 4, Lesson 19
Worksheets for Algebra 1

Summary

Given any function, how does adding a positive or negative value,k , to f(x) or x affect the graph of the parent function?

The value of the constant shifts the graph of the original function k units up (if k > 0) and k units down (if k < 0) if k is added f(x) to such that the new function is (x) = f(x) + k.

The value k of shifts the graph of the original function k units to the left (if k > 0) and kunits to the right (if k < 0) if is added to f(x) such that the new function is g(x) = f(x + k).

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