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anonymous
 one year ago
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).
anonymous
 one year ago
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@phi @radar @aloud @AutumnRoseT @xavierbo2 @Data_LG2 @mathmate @HWBUSTER00 @hartnn

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1@georgia545 @aloud Do you know the range of f(x)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434724687580:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So the range of y=cos(x) is [1,1] Are you familiar with the interval notation?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Check this out: http://www.coolmath.com/algebra/07solvinginequalities/03intervalnotation01

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah i do i just didnt know that was the name

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1range of y=[1,1] means the range of y can take any value between 1 and +1.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Multiplying y by 5 means stretching the function vertically and flipping it about the xaxis. so y=5cos(x) has a shape like this: dw:1434724951272:dw so what is the range of y=5cos(x)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1( 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/07solvinginequalities/03intervalnotation01 Don't skim it. Go through the details. Math is a very precise language because there is no redundance.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yes, [5,5] is the correct new range.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So which answer would it be because in f(x) it was [1,1] to [5,5] but thats not an option

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1That'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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it would be a because it went from [1,1] and shifted down 3 right?

Sachintha
 one year ago
Best ResponseYou've already chosen the best response.0It won't be A. Try again. :)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Did you say [1,1] translated down? Recall we have g(x)=5cos(x)3.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1We agreed it was [5,5] before translation, didn't we?

Sachintha
 one year ago
Best ResponseYou've already chosen the best response.0@georgia545 Don't look forward for a direct answer. Try to work it out following mathmate's instructions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i thought it started as [1,1] in f(x) then went to [5,5] in g(x) ????

Sachintha
 one year ago
Best ResponseYou've already chosen the best response.0The range of function g(x) is [5,5]. Then it is shifted down 3 units in the negative y direction.

Sachintha
 one year ago
Best ResponseYou've already chosen the best response.0Then the range also changes according to it.
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