Question

How do you graph `y=-cos2x`?

Answer 1

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

Explanation:

Given:

`color(red)(y = -cos 2x)`

We need to graph this function.

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

`color(blue)(y = cos x)`

`color(blue)(y = - cos x)`

`color(blue)(y = cos 2x)`

`color(blue)(y = -cos 2x)`

First, we will start graphing

`color(blue)(y = cos x)`

Then we will graph

`color(blue)(y = - cos x)`

Then we will graph

`color(blue)(y = cos 2x)`

Then we will graph

`color(blue)(y = -cos 2x)`

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 2x` is all Real Numbers: `RR`

The function has no undefined points nor domain constraints.

Therefore domain is `-oo < x < oo`

As the `- Cos 2x` 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.