How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function? The function shifts down 3 units, so the range changes from −1 to 1 in f(x) to −4 to −2 in g(x). The function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x). The function shifts down 5 units, so the range changes from −1 to 1 in f(x) to −6 to −4 in g(x). The function shifts down 5 units, so the range changes from −5 to 5 in f(x) to −10 to 0 in g(x).

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How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function? The function shifts down 3 units, so the range changes from −1 to 1 in f(x) to −4 to −2 in g(x). The function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x). The function shifts down 5 units, so the range changes from −1 to 1 in f(x) to −6 to −4 in g(x). The function shifts down 5 units, so the range changes from −5 to 5 in f(x) to −10 to 0 in g(x).

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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i really d know
okay thanks though
@georgia545 @aloud Do you know the range of f(x)?
0??
|dw:1434724687580:dw|
So the range of y=cos(x) is [-1,1] Are you familiar with the interval notation?
noo
Check this out: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01
oh yeah i do i just didnt know that was the name
range of y=[-1,1] means the range of y can take any value between -1 and +1.
Multiplying y by -5 means stretching the function vertically and flipping it about the x-axis. so y=-5cos(x) has a shape like this: |dw:1434724951272:dw| so what is the range of y=-5cos(x)?
(5,-5)?
( and ) means values of the limits are excluded, but don't apply here. Use [-5,5]. Intervals always go from smaller to larger values. Please review the link: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01 Don't skim it. Go through the details. Math is a very precise language because there is no redundance.
Yes, [-5,5] is the correct new range.
So which answer would it be because in f(x) it was [1,-1] to [5,-5] but thats not an option
That's because we have not considered the term -3 yet. g(x) = -5cos(x) -3. So do you know what the term would do? It would cause a vertical translation. -3 means a translation of 3 units in the negative y direction, and +2 means a translation up 2 units. I'll leave you with that. You can post for a check if you want.
so it would be a because it went from [1,-1] and shifted down 3 right?
It won't be A. Try again. :)
Did you say [-1,1] translated down? Recall we have g(x)=-5cos(x)-3.
We agreed it was [-5,5] before translation, didn't we?
@georgia545 Don't look forward for a direct answer. Try to work it out following mathmate's instructions.
i thought it started as [1,-1] in f(x) then went to [5,-5] in g(x) ????
The range of function g(x) is [5,-5]. Then it is shifted down 3 units in the negative y direction.
Then the range also changes according to it.

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