How do you graph #y=1/3 cosx#?

1 Answer
KillerBunny
Nov 6, 2015

You are modifing a function by scalar multiplication, i.e. you're going from #f(x)# to #lambda f(x)#, being #lambda# some real number.

This kind of changing only affects the amplitude of the function. In fact, if #cos(x)# ranges from #-1# to #1#, then #1/3cos(x)# will range from #-1/3# to #1/3#.

You can see that all the rest remains untouched, if #f(x_0)=0# for some #x_0#, then also #lambda f(x_0)# will be zero.

Moreover, also the derivatives are in the same relation, since #(lambda f(x))' = lambda f'(x)#, so #lambdaf(x)# is growing if and only if #f(x)# was growing too, and vice versa.

Of course, all I wrote applies when #lambda# is positive, otherwise you can switch #lambda# to #-lambda# and repeat everything about #-f(x)#.

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