Dr Duncan James > UPmaths > Graphs

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Graphs are a way of representing a rule such as "y is the same as x", "y is equal to x squared" or "x is always equal to 3". Really, it is that simple: the line on a graph represents a rule. At a more advanced level a way of thinking about graphs is that if an equation cannot be solved uniquely the graph is a way of representing the infinity of possible solutions.

Graphs Introduction

Graphs are, in general, a way of representing the infinite number of solutions to an unsolvable equation. Cool!

A graph shows pairs of values: left-and-right and up-and-down represent two different things.

Sketch or Solve (UP3)

To save time it makes sense to get used to common graphs.

Straight Line Graphs

A graph that is a straight line!

Playlists on the way. Request them if you want them soon!

What Different Gradients Look Like (YouTube)

Polynomial Graphs

Curved graphs with a predictable pattern depending on the index/power.

Graphs of Odd and Even Powers of Polynomial (YouTube)

Sketching Polynomial Graphs Slow Working (UP3)

Sketching Polynomial Graphs Quick Working (UP3)

More polynomial playlists on the way. Request them if you want them soon!

Other Common Graphs

Some other common types of equation have predicable shapes.

Playlists on the way. Request them if you want them soon!

Graph Transformations

Graph transformations are talked about in other sections of UPmaths. This is section just looks at this topic in a bit more detail.

Transformations of Graphs in Direction of x and y Axes (YouTube)

Order for Combining Transformations in Direction of x and y Axes (YouTube)

Graph Practice

It can be good to do quick-fire revision of all the common graph shapes.

Graph Sketching Mixed Difficult (UP3)

Graph Sketching Mixed (UP4)

Graph Sketching Mixed Difficult (UP4)

Graphs of Functions

A function is a pattern or relationship. Sometimes we do not know the equation or it may not have an equation.

Typical questions about graphs like this involve "transformations".

Transformations of Graphs of Functions (UP3)

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