I need help with this homework that has 2 steps thatI am extremely confused abou
ID: 3095916 • Letter: I
Question
I need help with this homework that has 2 steps thatI am extremely confused about. Can someone show step bystep? I need to graph it as well. Here is the problem: Starting from the function: f(x) = 2(x-3)2 +1 apply as few transformations as possible to turn it into: g(x)= x2 Then once that is done apply the reverse transformations andtur0-n g(x) back into f(x) showing the steps. Thanks! I need help with this homework that has 2 steps thatI am extremely confused about. Can someone show step bystep? I need to graph it as well. Here is the problem: Starting from the function: f(x) = 2(x-3)2 +1 apply as few transformations as possible to turn it into: g(x)= x2 Then once that is done apply the reverse transformations andtur0-n g(x) back into f(x) showing the steps. Thanks! Then once that is done apply the reverse transformations andtur0-n g(x) back into f(x) showing the steps. Thanks!Explanation / Answer
g(x) -> f(x) since it is easier to understandx^2 is a parabola passing through the origin and what not (iassume you know how to graph x^2)
When you do transformation, just look at each componentseperately, don't mesh them all together
x-3 (or the inner x) tell you whether it shiftleft or right, in this case it is -3 so it will shift right 3units
+1 in the end tell you whther the graph shift up or down, + 1in this case so it is shifting up, (if -1 then it is shiftingdown)
the 2 in 2(x-3)^2 (or any inner x for that matter) will tellyou how the curve will be twice as sharp (twice is just thedecription not real value) , (if it is 3 then the curve is sharperthan 2, i hope you get my point)
from f(x) -> g(x), think g(x) as (1/2)(2)(x-3+3)^2 + (1-1)= x^2
you would see that inner x has a + 3 (comparing with the f(x),x-3,) mean it shifts left 3 units), a -1 at the the end (comparing to the starting f(x)) hence itshift down 1 unit) the coef # is 1/2 hence the curve as half as sharp asf(x)