How do you translate #y=2sin (4x-pi/3)# from the parent function?
1 Answer
Start from
#sin(x)\to sin(4x)# #sin(4x)\to sin(4x-pi/3)# #sin(4x-pi/3)\to 2sin(4x-pi/3)#
Let's see how these changes affect the graph:
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When we change
#f(x)\to f(kx)# , we change the "speed" with which the#x# variable runs. This means that, if#k# is positive, the#x# values arrive earlier. For istance, if#k=4# , we have#f(4)# when#x=4# , of course. But when computing#f(4x)# , we have#f(4)# for#x=1# . This means that#sin(4x)# is a horizontally compressed version of#sin(x)# . Here's the graphs . -
When we change from
#f(x)# to#f(x+k)# , we are translating horizontally the function, and the reasons are similar to those in the first point. Is#k# is positive, the function is shifted to the left, if#k# is negative to the right. So, in this case, the function is shifted to the right by#pi/3# units. Here's the graphs -
When we change from
#f(x)# to#k*f(x)# , we simply multiply every point in the graph by#k# , resulting in a vertical stretch (expanding if#k>0# or contracting if#k<0# ). Here's the graphs.
