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# y=F(|x|) y=|f(x)| |y|=f(x) y=|f(x)+3| etc watch

1. Hiya, I was wondering if anyone can help me with functions, telling me what physical effects the below functions have on graphs would be really useful!
1) y=F(|x|)
2) y=|f(x)|
3) |y|=f(x)
4) y=|f(x)+3|

Also what difference does it make if it is y=f(x+3) rather than y=f(x) +3 which way does it shift in each case?

Also I'm kinda confused about the domain and range, is the range the possible y values and domain the possible x values or am i confused?

Thankyou!
2. 1) This means you only plot/sketch points for the +ve x-values, since you're taking the modulus. Before inputting into the function, you have to mod the 'x'. This in effect means none of the -ve x-values get plotted.

2) First sketch the graph of f(x), and then reflect all -ve values of f(x) (parts under the x-axis) in the x-axis. You do this, because you are taking the modulus of f(x), therefore f(x) does not have a negative value.

3) Same as 2), but reflect negative parts of 'x' in the y-axis.

4) Same as 2). But your sketch will be slightly different. I'll explain that bit now...

f(x+3), means you shift the graph 3 units to the left.
f(x) + 3, means you shift the graph 3 units upwards.
3. thats is really helpfull, thankyou!!!
4. (Original post by mockel)
3) Same as 2), but reflect negative parts of 'x' in the y-axis.
This isn't right surely

If you have a graph of y = f(x), well there will be no graph for those parts where f(x) < 0. For those parts of the graph where f(x) >= 0 the graph of |y|=f(x) will include these bits of the graph and their reflections in the x-axis
5. (Original post by mockel)
1) This means you only plot/sketch points for the +ve x-values, since you're taking the modulus. Before inputting into the function, you have to mod the 'x'. This in effect means none of the -ve x-values get plotted.
And this part as well, I'm afraid I don't agree

Take your graph of y = f(x), chop off the x<0 part and then the graph of y=f(|x|) includes the half you have left and its reflection in the y-axis
6. (Original post by RichE)
And this part as well, I'm afraid I don't agree

Take your graph of y = f(x), chop off the x<0 part and then the graph of y=f(|x|) includes the half you have left and its reflection in the y-axis
Yeh..I agree
7. http://www.ajimal.com/mathematics/alevel/mappings.pdf

That might help !

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