Hi, we are given a graph. say it is y = 6 (x-3)^2 +5 When I look at the graph, I understand how to find out the 3 and 5 but how would I determine that theres a vertical stretch by a factor of 6, when looking at the graph. And, when you explain to me how it works, is it the same for the rest of the types of graphs, like y = |x| for ex? Thats really the only thing I can't understand, can you show me an example by posting a link to show me?? Thanks in advance.
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you are assuming that you recognize a BASIC function
thus if y = f(x) is the basic and you now have y1 = A f(x) then
if | A | > 1 you have a vertical stretch while if | A | < 1 then a vertical compression
if y2 = f( a x ) and | a | > 1 you have a horizontal compression
while | a | < 1 means horizontal stretch
if y3 = A f(w x) + B then you can have vertical stretch / compression as well
horizontal stretch / compressions and the B means taking the
resulting graph up { B > 0 } or down { B , 0 }
if y = cos x and y1 = 3 cos ( 2x ) - 5 you compress the original graph horizontally 1st ,
then stretch this result by 3 in the vertical direction and finally
dropped the last graph 5 units
thus if y = f(x) is the basic and you now have y1 = A f(x) then
if | A | > 1 you have a vertical stretch while if | A | < 1 then a vertical compression
if y2 = f( a x ) and | a | > 1 you have a horizontal compression
while | a | < 1 means horizontal stretch
if y3 = A f(w x) + B then you can have vertical stretch / compression as well
horizontal stretch / compressions and the B means taking the
resulting graph up { B > 0 } or down { B , 0 }
if y = cos x and y1 = 3 cos ( 2x ) - 5 you compress the original graph horizontally 1st ,
then stretch this result by 3 in the vertical direction and finally
dropped the last graph 5 units