How do you translate the graph of #y=cosx+3#?

1 Answer
Daniel L.
Aug 20, 2017

You have to translate a graph of #y=cosx# #3# units up. See explanation.

Explanation:

The general rule of translating graphs of functions is:

To get a graph of a function:

#f(x-a)+b#

from the graph of #f(x)# you have to translate it by a vector

#vec(u)=[a,b]#

In the given example the base function is

#f(x)=cosx#

The result function does not have #a# coefficient (nothing is added or subtracted from #x#), but it has #b# coefficient because the value (3) is added to the whole function, so the resulting vector is:

#vec(u)=[0,3]#

The vector's #y# coordinate is #3#, so the graph is moved 3 units up along Y axis

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