Domain and range of a function?

Question

Which of the following is the domain and range of

f(x) = 2cos(4x + pi) -1 ?

i think the domain is (-infinity, infinity) but also, there is the answer (-pi, pi) so that is confusing me bc this is a trig function. i'm not sure. what is the correct one, if either is even correct (bc i could be VERY wrong)

and i still dont understand how to find the range? no one is really explaining to me, just giving me the answer.

Answer 1

You have the domain right; (-infinity, infinity).

Range is all the Y values the sinusoidal graph will touch. This is easy for the most part. Take the "A" value, or amplitude. In this case, it is 2. This would mean the graph would initially have a range of (-2,2). With the (-1) shift though, the graph shifts down one on the Y-axis. This makes our new range (-3,1).

If you need more help with range, feel free to ask.

Answer 2

To understand domain and range of this function, you need to understand cos(x). The range of cox(x) unchanged is (-1 to 1).

cos(ax +b).......a will make the period longer or shorter and b will shift it. Anything inside will not affect range, since range is the y value.

x can be anything in this case, so you have the domain correct.

acos(x)....... a will make the amplitude of the wave increase or decrease by that factor. In this case we have a=2. so 2cos(x) would mean that the height of the wave goes up to 2 and down to -2 within the graph. So if the equation were 2cos(x) the range would be -2 to 2.

cos(x) + a.......This will shift the entire graph up or down depending on a. In your equation it is -1. So the graph will shift 1 down. So instead of the peaks being at 2 and the low being at -2...you subtract -1 from each. 1 is the max and -3 is the min.

Range is -3 to 1.