College Algebra

2.7

Transformations

Objectives

Use vertical and horizontal shifts to sketch graphs of functions.

Use reflections to sketch graphs of functions. Use compressions or stretches to sketch

graphs of functions.

Shifting Graphs

If c is a positive real number, then the graph of y= f(x) is shifted as follows:

1) vertical shift c units up f(x)+c 2) vertical shift c units down f(x) – c 3) horizontal shift c units to the right f(x-c) 4) horizontal shift c units to the left f(x+c)

Examples

Reflecting Graphs

1) Reflection in the x-axis -f(x) 2) Reflection in the y-axis f(-x)

Nonrigid Transformations

1) Vertical stretch cf(x), c >1 2) Vertical shink cf(x), 0<c<1 3) Horizontal shrink f(cx), c>1 4) Horizontal stretch f(cx), 0<c<1

assignment

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