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I really struggle with this, what are all the different functions I need to know for the exam? using the y = f(x) graphs? I'm on the edexcel exam board:)
I'm doing AQA, but it should be similar.
I was struggling with that too. But you need to unfortunately, memorize them. Basically, I look at 'b' as 'x' (as it moves the graph right or left) and 'a' as 'y' (as it makes the graph moves up or down).
1. f(x)+a In vector form: (0,a)The 'a' means the graph y=f(x) moves 'a' units up or down, depending if a is positive or negative.
2. f(x+b) In vector form: (b,0) The graph moves 'b' units right or left. But be careful here. If it is f(x-3), x-3=0, x=3. So graph moves 3 units to the right. f(x+5), x+5=0, x= -5. So graph moves 5 units to the left.
3. f(x+b)+a In vector form (b,a) The graph moves 'b' units right/left, and 'a' units up/down.
1. f(-x) is a reflection of f(x) in the y-axis.
2. -f(x) is a reflection of f(x) in the x-axis.
d(fx) means f(x) times by the number 'd'. This makes the graph stretch by scale factor 'd'. so if f(x)=x+1 and 'd'=2, then when drawing the graph find 'x' the usual way, and then times it by 'd', which in this case is 2.
f(cx) means 'x' times the number 'c'. An easier way to look at this is 1/c(fx). It becomes like this after you invert the 'c' and put it on the outside. This makes the graph stretch by scale factor 1/c. So if the equation is f(2x), it actually means 1/2(fx). So half the normal graph.
Hope this all makes sense! If you have any questions, just ask.