Range of a Cosine Function...?

Question

I need to know what the range of the function: f(x)=2cos(x/3+x/6)-4 is.

I have a guess, but I'm not sure if I'm right or not. I don't have my notes [sad, I know], so I can't refer to those. The answer I have doesn't look familiar, I tried to search online, couldn't find it, so the person with the best answer will get 'Best Answer' because I really need to answer this math problem lol. THANX.

Answer 1

amplitude is 2
it shifts down 4

therefore, the range is [-4-2,-4+2]

equals [-6,-2]

Answer 2

Normally, the range of f(x) = cos(x) is [-1, 1].

The range of f(x) = 2cos(x) stretches the graph and therefore the range as well; this function's range is [-2, 2]

For the function f(x) = cos(x) + 1, the range shifts to [-1 + 1, 1 + 1], or, quite simply, [0,2].

What you have is a combination of the graph stretching vertically, and a shift; f(x) = 2cos(x/3 + x/6) - 4 would have a range of
[-2 - 4, 2 - 4], or [-6, -2]

If you'd like to know the range of a sine or cosine function in general, it will be, for

f(x) = a sin(bx + c) + d

Your range will be [ -|a| + d, |a| + d ], where

| | means absolute value.

If you're wondering what role the (x/3 + x/6) played in the range ... it plays no role. The role that it DOES play in is the function's period.

Answer 3

The range is only affected by the multiplier outside the cosine function. In this case, it would be 2. Since cosine has only a normal range between 1 and -1, then multiplying it by 2 would increase these boundaries to a range of between 2 and -2.

Now, I define range as the Y axis so I am not positively sure that this may help you if you happen to have a different definition. Range is usually the Y axis and the period of the function is the X axis in which a normal cosine function has a period of 2pi.

I hope this helps.

Answer 4

The maximum and minum values returned by a Cosine function is ±1. Using those two extreme values you can find the range of the function by substituting Cosine with those values.

2(-1) - 4 = -2 - 4 = -6

2(1) - 4 = 2 - 4 = -2

So the range of the function is [-6,-2].

Answer 5

The most the cos of any thing can be is 1. The least it can be is -1.

range is -2 to -6

Answer 6

x/3 + x/6 = (2x + x)/6 = 3x/6 = x/2

The range of the cosine function is [-1,1], and as x goes from 0 to 4*pi, cos(x/2) takes on all values in this range. Therefore,
2cos(x/2) takes on all values in the interval [-2,2], and so f(x)=
2cos(x/2) - 4 take on all values in the interval [-6,-2].
The range of f(x) is [-6,-2].

Answer 7

By definition, range stands for all y values.

Since the range of cos() is from -1 to 1, the range of f(x) is from -6 to -2.

Hope it helps.

Answer 8

f(x) = 2cos(x/3 + x/6) - 4 = 2cos( x/2 ) - 4

we know that:

-1 =< cos(A) =< +1
so: -1 =< cos(x/2) =< 1
-2 =< 2cos(x/2) =< 2
-2 - 4 =< 2cos(x/2) - 4 =< 2 - 4
=> -6 =< 2cos(x/2) - 4 =< -2
=> -6 =< f(x) =< -2

Answer 9

let me ask someone else