Ok, I need major help fast in Math.?

Question

Ok, i'm taking AP Calc, and we have to do some easy summer work (although I shouldn't be calling it easy if I'm having trouble with it). I have a few questions about transformations, If you are good at math PLZZZ take a couple of minutes to help me. Post before the 27th please, because my school starts on the 28th.

Ok, I am given a graph of a line. Just so you know some points, the y-intercept is at (0,4) and the x-intercept is at (-3,0).

Now, this line is f(x), right. I need to draw the transformations of this graph. The first one is -3f(x), second one is f(-3x). Please help me understand this by telling me how the x and y values are affected when you multiple the F(x) by -3 in the first one, and when u multiply the x by -3 and then take the function at that point.

Ok, sorry but if you can also explain how to do 4f(x), and f(4x) Thanks.

If you can explain it well, and give me the coordinate points, THANKS A LOT :P and you'll get 10 points and a warm feeling inside loll.

Answer 1

Well, f(x) is the function of the line.  f(x) = (4/3)x + 4

-3f(x) would just be -3 times the whole function. -3f(x) = (-12/3)x - 12 = -4x-12.  so thats a line through (0,-12) and (3,0)

to find f(-3x) you will need to take your original f(x) and multiply -3 to x.

f(-3x) = (-12/3)x + 4 = -4x +4.  That is a line through (0,4) and (1,0)

Answer 2

as far as attempting to help you...

for the 4f(x) id finish it out with the f(x) =mx+b thing

you know filling in the coordinate with the slope[you have to use the equation so find it] then fill in the y intercept..

then id divide both sides by 4 so you have a standard f(x) and the other side would be divided by 4 as well..

so thats how id get that one..

and for the 2nd one...

since its f(4x) id assume it 4 times x

so id do the same as i said to do in the first problem...get the f(x) =mx+b with the slope and y intercept.

THEN id multiply the functon by 4...since its 4x...

i can show you the work if youd like O.o

although idk if im exactly right

and for the -3f(x) and f(-3x) do the same

work:

so you do the slope equation y2-y1/x2-x1

and get the slope as 4/3 the plug in the slope and the coordinates (0,4) to get 4=4/3(0) + b

and that makes b=4 so then you fill it in and get -3f(x)=4/3x + 4 and you divide that by -3 to get f(x) =-4/9x - 4/3 and thats easily graphable

work:

do the same thing and get that f(x)=4/3x + 4

and just multiply it by -3 to get f(x) = -4x - 12

then grapg

again idk if its right...im only 15 but i think i got it :]