Chapter 2 - functions and graphs

All knowledge and key words for Edexcel A2 textbook Pure.

What is a function?

When every input has a distinct (single) output.

What are the types of function?

• one to one

• many to one

What is the range of f^-1(x)?

The domain of f(x)

What is the domain of f^-1(x)

The range of f(x)

What is a domain?

All the values x can take (in f(x))

What is a range?

All the values the function can take (y in y = f(x))

How to translate f(x+a)

Horizontal translation -a

How to translate f(x)+a

Vertical translation +a

How to translate f(ax)

Horizontal stretch scale factor 1/a

How to translate af(x)

Vertical stretch scale factor a

How to translate f(-x)

Reflect f(x) in the y-axis

How to translate -f(x)

Reflect f(x) in the x-axis

When f(x) >= 0 what is modulus f(x)?

Modulus f(x) = f(x)

When f(x) < 0 what is modulus f(x)?

Modulus f(x) = -f(x)

What is ff(x)?

Just like gf(x) but with f.

What is ff^-1(x)?

ff^-1(x) = f^-1f(x) = x

How is f^-1(x) represented graphically?

Reflection of f(x) in the line y=x

If f(x) is many-to-one, then what would f^-1(x) be?

• not a function

• because it would be one-to-many