\( \DeclareMathOperator{cosec}{cosec} \)

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Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Graph Patterns Find the equations which will produce the given patterns of graphs.
- Transformations of Functions A visual aid showing how various transformations affect the graph of a function.

Here are some exam-style questions on this statement:

- "
*The graph of the curve A with equation \(y=f(x)\) is transformed to give the graph of the curve B with equation \(y=5-f(x)\).*" ... more - "
*(a) By completing the square, solve \(x^2+8x+13=0\) giving your answer to three significant figures.*" ... more - "
*The graph of the following equation is drawn and then reflected in the x-axis*" ... more - "
*(a) Find the interval for which \(x^2 - 9x + 18 \le 0\)*" ... more - "
*(a) Write \(2x^2+8x+27\) in the form \(a(x+b)^2+c\) where \(a\), \(b\), and \(c\) are integers, by 'completing the square'*" ... more - "
*Part of the function of \(y=f(x)\) is shown in the following diagram.*" ... more - "
*Let \(f (x)=a(x-b)^2+c\). The vertex of the graph of \(f\) is at (4, -3) and the graph passes through (3, 2).*" ... more - "
*A function is defined as \(f(x) = 2{(x - 3)^2} - 5\) .*" ... more - "
*\(f\) and \(g\) are two functions such that \(g(x)=3f(x+2)+7\).*" ... more - "
*Let \(f(x)=5x^2-20x+k\). The equation \(f(x)=0\) has two equal roots.*" ... more - "
*Let \(f(x) = {x^2}\) and \(g(x) = 3{(x+2)^2}\) .*" ... more - "
*Let \(f\) and \(g\) be functions such that \(g(x) = 3f(x - 2) + 7\) .*" ... more - "
*Two functions are defined as follows: \(f(x) = 2\ln x\) and \(g(x) = \ln \frac{x^2}{3}\).*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Functions A relationship between two sets can be called a mapping. Elements of the first set (domain) are mapped to elements of the second set (range). A function is a special type of mapping for which one value in the domain maps to one, and only one value in the range.Pupils in Primary school will use the concept of function machines to perform calculations. They will then learn to ‘work backwards’ to find the inverse function. The study of functions becomes more formal as pupils become more proficient and able to cope with more complex mathematical ideas.
- Graphs This topic includes algebraic and statistical graphs including bar charts, line graphs, scatter graphs and pie charts. A graph is a diagram which represents a relationship between two or more sets of numbers or categories. The data items are shown as points positioned relative to axes indicating their values. Pupils are typically first introduced to simple bar charts and learn to interpret their meaning and to draw their own. More sophisticated statistical graphs are introduced as the pupil's mathematical understanding develops. Pupils also learn about coordinates as a pre-requisite for understanding algebraic graphs. They then progress to straight line graphs before learning to work with curves, gradients, intercepts, regions and, for older pupils, calculus.

This video on Transformation of Functions is from Revision Village and is aimed at students taking the IB Maths AA Standard level course

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.