# Manipulating Graphs: Shifts and Stretches

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More Lessons for College Algebra

Math Worksheets

A series of college algebra lectures.
How to transform a graph horizontally or vertically?
How to vertically or horizontally stretch or compress a graph?

How to transform a graph horizontally?
f(x) &rarrow; f(x + k)
shifts f(x), k units horizontally.
if k > 0, the shift is to the left.
if k < 0, the shift is to the right.

How to transform a graph vertically?
f(x) &rarrow; f(x) + k
shifts f(x), k units vertically.
if k > 0, the shift is upwards.
if k < 0, the shift is downwards.

Horizontal and Vertical Graph Transformations
Shifting Curves along Axes
Transformations of Parent Functions
Vertical Shifts and Horizontal Shifts

How to vertically stretch or compress a graph?
y = af(x), a > 1, will stretch the graph of f(x) vertically by a factor of a.
y = af(x), 0 < a < 1, will compress the graph of f(x) vertically by a factor of a.

How to horizontally stretch or compress a graph?
y = f(bx), b > 1, will compress the graph of f(x) horizontally.
y = f(bx), 0 < b < 1, will stretch the graph of f(x) horizontally.

Function Transformations: Horizontal and Vertical Stretches and Compressions
This video explains to graph graph horizontal and vertical stretches and compressions in the form af(b(x - c)) + d. This video looks at how a and b affect the graph of f(x).
Using Transformations to Graph Quadratic Functions

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