Functions (AQA GCSE Further Maths)

A function f is given by

A sketch of is shown.

Work out all the values of for which  .

A function is given by 

Draw the graph of on the grid.

Solve 

You must show your working.

The domain of is

Work out the range of .

     for all values of 

     for 

Work out the range of .

Give your answer as an inequality.

Work out the range of .

Give your answer as an inequality.

Solve  =g

You must show your working.

Give your answers to 3 decimal places.

 for positive values of .

Work out   

Give your answer as a fraction in its simplest form. You must show your working.

The function is given by   

The range is 

Work out the domain of the function.

The function is given by with domain

Work out the range of the function.

The function h is given by 

Work out.

where  is a constant.

Given that  work out the value of .

is a function such that  

Work out an expression for .

is a function such that

Work out an expression for  .

is a function with domain all values of .

 where is a constant.

Work out the possible values of . Give your answer as an inequality.

For each of these two function machines, when the input is  the output is .

   and        and     

Work out an expression for  in terms of .

Give your answer in its simplest form.