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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) → 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) → 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

The following diagram shows some examples of vertical stretch and compress of graphs. Scroll down the page for more examples and solutions on stretching and compressing of graphs.

**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).**Graphing Quadratics Using Patterns**

Using Transformations to Graph Quadratic Functions

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) → 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) → 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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