Functions

__**Functions**__


 * 10th September 2012**

Bit of a 'teacher heavy' lesson today - lots of definitions.

Here is the lesson:

Basically...

The DOMAIN is the set of all values that can go IN The RANGE is the set of all values that can come OUT - often the best way to ascertain this is to draw a graph. Completing the square (for a quadratic) can be very useful.

Four different types of mappings: 1 - 1, 1 - many, many - 1, many - many

If a mapping is 1 - 1 or many - 1 (ie you KNOW the output if you know the input) then it is a FUNCTION

'failing the vertical line test' is a good way to decide if a mapping is NOT a function.


 * Wednesday 12th September**

Transforming functions. You need to be able to recognise translations and stretches, both vertical and horizontal. Also - reflections in the x- and y- axes. Generally - if you have a combination of transformations, make sure you 'change the shape' (stretch) before you move the graph. Here is the lesson:


 * Monday 17th September**

A bit more of transforming functions, especially quadratics. The order in which you do the transformations can be really tricky. Double check by looking at the turning point, y-intercept or roots - when you sketch a function EVERY aspect needs to make sense!

Then we moved onto COMPOSITE functions. The key thing to remember here is that fg(x) means do g(x) first, then do f to what you get. ie fg(x) means 'f of g of x'. Lesson:


 * Wednesday 19th Sep**

Today we looked at inverse functions. You can find the inverse function by rearranging to make x the subject of y = f(x).

Graphically - the graph of f -1 (x) is a reflection of the graph of f(x) in the line y = x

The domain of f(x) is always the same as the range of f -1 (x) The range of f(x) is always the same as the domain of f -1 (x)

If a function f(x) is one-to-one then then inverse of f(x) is also one-to-one (ie a function) If a function f(x) is many-to-one then the inverse is one-to-many (ie NOT a function). In order to 'uniquely define' the inverse, we can restrict the domain of f(x), thus making it one-to-one (you can think about the horizontal line test!)

I'll put today's lesson here when I can:

Homework sheet (Functions 1) due in Monday 1st October - do it as well as you can please!