TMUA Topic Menu

TMUA Topic 8. Graphs of Functions

Exam Techniques

This topic underpins many of the other topics in the TMUA specification, and therefore any questions on other topics could involve some sort of graph sketching. The specification sets out the standard functions that you should know and be able to sketch quickly and easily. As part of your preparation, it can be helpful to play around with an equation in a graph drawing package such as DESMOS to see what happens to the graph as you change the coefficients.
 

You must be able to recognise translations, reflections and enlargements of these standard graphs, and also combined transformations. You should understand what happens to the position of roots, stationary points, intercepts etc, under these transformations. In addition, make sure you understand the modulus function, and how to sketch this, so you can deal with modulus questions graphically as well as algebraically. 
 

You should understand the following terms in relation to graphs: root, intercept, maximum, minimum, point of inflexion, concave, convex, increasing, decreasing, asymptote, even/odd function, and periodic function.
 

You should also be able to determine compound functions such as fg(x) and understand the importance of the order of calculation. 
 

Some questions may require you to match an equation to a set of graphs, and for this you may need to consider the position of the intercepts, stationary points, roots, any asymptotes, and also the behaviour of the graph for large x  (eg does the graph tend to a limit or to positive or negative infinity?).