# How do you graph y=-cos2x?

Jan 29, 2018

See the explanation, please. By observing graphs we can understand how transformation takes place.

#### Explanation:

Given:

$\textcolor{red}{y = - \cos 2 x}$

We need to graph this function.

To understand the behavior of this graph, we can draw the following graphs and then compare them:

$\textcolor{b l u e}{y = \cos x}$

$\textcolor{b l u e}{y = - \cos x}$

$\textcolor{b l u e}{y = \cos 2 x}$

$\textcolor{b l u e}{y = - \cos 2 x}$

First, we will start graphing

$\textcolor{b l u e}{y = \cos x}$

Then we will graph

$\textcolor{b l u e}{y = - \cos x}$

Then we will graph

$\textcolor{b l u e}{y = \cos 2 x}$

Then we will graph

$\textcolor{b l u e}{y = - \cos 2 x}$

Next, we will observe all of the above graphs as one:

KEY for the graphs:

Now the graphs ...

We observe the following in the graph of color(blue)(y = -Cos 2x

The domain of $- \cos 2 x$ is all Real Numbers: $\mathbb{R}$

The function has no undefined points nor domain constraints.

Therefore domain is $- \infty < x < \infty$

As the $- C o s 2 x$ function repeats itself, it is Periodic.

To be precise, the function color(blue)(y = Cos x  is Periodic with Period: color(blue)(2pi

The function color(blue)(y = - Cos x  is also Periodic with Period: color(blue)(2pi.

The function color(blue)(y = -Cos 2x  is Periodic with Period: color(blue)(pi.

Amplitude of the function color(blue)(y = - Cos 2x  is $1$.

If a point color(green)((x,y) lies on the graph, then the point color(green)((x+2kpi,y) will also lie on the graph, where color(green)(k is any integer value.