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

Aug 20, 2017

You have to translate a graph of $y = \cos x$ $3$ units up. See explanation.

#### Explanation:

The general rule of translating graphs of functions is:

To get a graph of a function:

## $f \left(x - a\right) + b$

from the graph of $f \left(x\right)$ you have to translate it by a vector

## $\vec{u} = \left[a , b\right]$

In the given example the base function is

## $f \left(x\right) = \cos x$

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:

## $\vec{u} = \left[0 , 3\right]$

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