MHB What Is the Domain and Range of y=cos(3(x - 45°)) +2?

[mathuravasant]

State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.

 

[jonah1]

Beer induced request follows.

State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.

Please show us what you have tried and exactly where you are stuck.
We can't help you if we don't where you are stuck.

 

[mathuravasant]

like how do you find domain and range off from that given equation I just don't know what to do

 

[topsquark]

like how do you find domain and range off from that given equation I just don't know what to do

You are having a great deal of trouble with these. I suspect the biggest cause isn't in the problems but in the definitions. I would suggest having a 3 x 5 card (or some other modern equivalent) stating what the domain, range, frequency, wave number, horizontal shift (or phase), and vertical shift are for each.

[math]y = cos( 3(x - 45) ) + 2[/math].

What is the domain? It's the interval on the x-axis that the function is defined on. So one cycle is 360 degrees. Thus
[math]0 \leq 3(x - 45) \leq 360[/math]
So what are the possible values for x? [math]0 \leq 3(x - 45)[/math] to [math]3(x - 45) \leq 360[/math]

What is the range? It's the interval on the y-axis that the function takes on over the domain. So for the sake of argument let's say that the domain is [math]-45 \leq x \leq 90[/math]. (Mind you, it isn't.) Then what is the range of cosine? It's best to graph this one and take a look since cosine "waves" so graph [math]y = cos( 3(x - 45) ) + 2[/math] and find the biggest change in y value for [math]-45 \leq x \leq 90[/math].

Let us know how it goes.

-Dan