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?

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.

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

Transformations of Parent Functions

Vertical Shifts and Horizontal Shifts

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.

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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