A variable, e.g. x, represents an unknown number.

A function, e.g. f(x) (which is read as “F of x”, or “Some function of x”), is like a ‘super variable, representing not just an unknown number, but a whole expression, such as 2x2 + 5x + 8, or 3x, or 4x – 2, or x2.

These functions are usually plotted as algebra graphs, and when we talk about ‘transforming’ them, we mean moving all the points up, down, left or right, or reflecting the function in the x or y axis, or squishing all the points closer together, or stretching them out.

Without redrawing the function, we can describe the transformation mathematically by rewriting the y = f(x) (which is sometimes referred to as the graph of fx) like this:

y = f(x + a) + m  Meaning subtract a from all of the original x coordinates, and add m to all of the original y coordinates

y = nf(bx)  Meaning divide all of the original x coordinates by b, and multiply all of the original y coordinates by n.

It can be thought of in general as “Whatever is inside the brackets, do the opposite to the new x-coordinates, and whatever is outside the bracket, do exactly what it says to all of the new y-coordinates.”

y = f(-x)  Represents a reflection in the y-axis, i.e. all new x-coordinates have their signs flipped

y = -f(x)  Represents a reflection in the x-axis, i.e. all new y-coordinates have their signs flipped

Nothing in this section yet. Why not help us get started?

Nothing in this section yet. Why not help us get started?

## Related Topics

Requires a knowledge of…

## Related Questions

• 1
Vote
4

### What is a coordinate grid?

By Ryan McGuire on the 10th of January, 2013

• 1
Vote
3

### What is the general form for a quadratic equation?

By Filsan on the 10th of January, 2013

• 1
Vote
2

### What does the graph of Y = x Linear look like?

By Filsan on the 10th of January, 2013

• 1
Vote
3

### What is the equation of a straight line graph?

By Filsan on the 10th of January, 2013

• 1
Vote
3

### What is the difference between a linear equation and a cubic equation?

By Filsan on the 10th of January, 2013

• 1
Vote
4

### What's the highest common factor of 36, 54 and 72?

By Verity Painter on the 8th of January, 2013

• 0
4

### How do I find 15% of a value?

By Verity Painter on the 8th of January, 2013

• 1
Vote
2

### What is an index law?

By Filsan on the 6th of December, 2012

• 0
1