# How do you graph  y=3-cosx?

Nov 4, 2017

Plot $\cos \left(x\right)$
then reflect in the X-axis to get $- \cos \left(x\right)$
and finally shift all point up $3$ units to get $3 - \cos \left(x\right)$

#### Explanation:

I have assumed that you are familiar with the graph for $\textcolor{red}{y = \cos \left(x\right)}$:

Reflecting this in the X-axis causes every $y$ coordinate to be come the negative of what it was for $\textcolor{g r e y}{y = \cos \left(x\right)}$;
that is we get $\textcolor{red}{y = - \cos \left(x\right)}$

Then adding $3$ to every $y$ coordinate increases each $y$ value of $\textcolor{g r e y}{y = - \cos \left(x\right)}$ by $3$ to give $\textcolor{red}{y = 3 - \cos \left(x\right)}$