Question

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

Answer 1

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