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 Posted: Sun Nov 01, 2009 6:49 pm
I am having a big dilemma. I try really hard to take notes in class and pay attention, but for some reason I have lots of trouble retaining things. D; We're currently working on functions in graphs.
For the problems I'm working on, we're given a graph with the coordinate points:
(-2, 3)
(1, 2)
and
(2, 0)
The points are all connected. The problem says:
Use the graph of y=f(x) shown to sketch the graph of the given function.
And then I am given something to work with. I can kinda do the ones where it gives me things like:
y=f(x+2)-3
and
y=f(x-4)+1
...on my calculator, but then I get ones like:
y=1/2*f(x)
and
y=-3*f(x)
...And I don't know what to do.
-----
Any help or in-depth explanation would be very appreciated, it's so frustrating to try so hard and then consistently do badly on tests because I have trouble retaining things and understanding. It also doesn't help much that I'm kinda shy and have trouble working up the nerve to ask questions when I need to most.
I've been trying super hard because we're having a test on Wednesday that'll pretty much make or break my grade for the quarter. Thanks to whoever tries to help me.
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Posted: Sun Nov 08, 2009 3:53 pm
ok 1st we gotta think about what this means.
some function takes each of these x's and turns them into y's
right now we don't know what that function is but that's ok
so lets look at what is happening here
we take -2 arrow put it in the function machine arrow out pops 3
1 arrow goes in the machine arrow 2
and
2 arrow goes in the machine arrow 0
ok we can think of this machine like f(x) so lets think about what your equations are doing to the number
y=f(x+2)-3
ok so the 1st time we put -2 (which is our x) into the function/machine now this time we put x+2 into the function/machine which in this case -2 becomes 0 then 1 becomes 3 and 2 becomes 4, so if you were just going to draw the graph of f(x+2) all the points would have the same y's but the x coordinate is shifted to the right two space for each one.
ok so if we were looking at f(x)-3 this time we are looking at what pops out of the function and subtracting 3. So 3 pops out of the 1st function so it becomes 0. 2 becomes -1 and 0 becomes -3. So just graphing f(x)-3 you have the x's stay the same but all the y coordinates are shifted down 2 spaces
the net effect of all this is every point when put in f(x+2)-3 moves to the right two spaces and down 3.
y=f(x-4)+1
this problem is similar to the 1st one, but in this case the problems are being shifted left 4 spaces and up one. Check this for yourself.
y=1/2*f(x)
This problem is slightly easier, because this time instead of manipulating both x and y, we are only changing the outcome of the function, which is y. So this equation says to multiply all the y's by 1/2. So 3 becomes 3/2. 2 becomes 1 and 0 stays 0. If you plot the points of this graph you'll see what happens is the graph kinda shrinks. Again, x stays constant.
y=-3*f(x)
This problem is similar to the 3rd one except you get an inverted graph that's "stretched out". Check this yourself
The basic lesson to take away from this is if there are functions effecting x they are inside the parenthesis {f(x+5), f(5x), f(x/2)} and the functions effecting y are outside of f(x) {2+f(x), -4f(x), f(x)/2}
hope this helps =3
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