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add 2 to every y value
you get the same curve, but slid up 2
so it would be 2=f(x)+2?
they want you to graph y= f(x)+2 that means put dots on the graph at certain points. For example, you put a dot at x= 0 y= -1+2=1 that is 2 up from where the original dot is. then connect the dots
i see what your saying. but do i use the points given to me or do i choose my own?
the instructions say use the graph of f. So you have to use f(x) that means find where the dot is for x=0 (it is at y=-1), add 2 to the y value, and plot it. that is what y= f(x)+2 means. Do it for every x where f(x) has a dot
okay i see. thank you very much
x is always constant correct
you do not change the x, just the y value.
okay. im doing y=-f(x) using the same graph so with (0,1) x=0 y=-(-1) ?
correction *with (0,-1)
OK, that's right. you should get a graph that slopes down
would it not be the same as the original though
how can it be the same when you are changing it? plot it and see.
the points come out on the same line as the first equation (y=f(x)+2)
what points did you get? here are the first two pair: original new 0,-1 0,1 1, 0 1,0
i got the same thing also. i guess i am just confusing myself
what did you get for the rest of the points?
(3,-1),(4,-2) i get it now
now with the same graph how would y=f(x-2) i understand with (0,-1) x=2+(0)=2 but how would y= work out?
y= f(x-2) is short-hand for pick x, for example x=2, now find the y value of f(x-2)= f(0) which is -1 (using the original function). so your point is (2,-1) for x=3, find the y-value of f(3-2)= f(1) = 0, so your next pair is (3,0) and so on. Notice that you can not find values for x=0 or x=1 because you do not know what f(-2) or f(-1) is. But you can find numbers for x=6. The whole graph is shifted to the right 2 spaces.
so if i have (3,4) , y=f(x-2) then say x=3 , and to find y i would substitute the x. y=3-2=1so my answer would be (3,1)
This is not right: y=3-2 what you want is y= f(3-2) that means y= f(1). y=f(1) means look at your graph and at x=1 what is the graph's y value? In your graph it is 0. so the answer is (3,0)
i don't really get it. in my precall book for point (0,-1) , y=f(x-2) x=0 y=f(0-2)....y=f(-2) (0,-2) ^^i feel this is incorrect
You must not be reading my posts very closely. See up above. But you are doing it correctly. You do not have any point to plot at x=0. No problem. Keep going until you get an x that works, and then keep going....
btw f(-2) is NOT-2, it is undefined. your point is (0, ???). Try x=2, which is the first x that will work.
okay il review everything over. oh okay . thank you again
using your graph, y=f(x-2) will give you the points 2,-1 3,0 5,1 6,2