How do you graph #y=-cos2x#?

1 Answer
Jan 29, 2018

Answer:

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)#

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Then we will graph

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

enter image source here

Then we will graph

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

enter image source here

Then we will graph

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

enter image source here

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

KEY for the graphs:

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Now the graphs ...

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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.