anonymous
  • anonymous
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@phi @radar @aloud @AutumnRoseT @xavierbo2 @Data_LG2 @mathmate @HWBUSTER00 @hartnn
anonymous
  • anonymous
was up
anonymous
  • anonymous
help mee?

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More answers

anonymous
  • anonymous
i really d know
anonymous
  • anonymous
okay thanks though
anonymous
  • anonymous
@mathmate ?
mathmate
  • mathmate
@georgia545 @aloud Do you know the range of f(x)?
anonymous
  • anonymous
0??
mathmate
  • mathmate
|dw:1434724687580:dw|
mathmate
  • mathmate
So the range of y=cos(x) is [-1,1] Are you familiar with the interval notation?
anonymous
  • anonymous
noo
mathmate
  • mathmate
Check this out: http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01
anonymous
  • anonymous
oh yeah i do i just didnt know that was the name
mathmate
  • mathmate
range of y=[-1,1] means the range of y can take any value between -1 and +1.
mathmate
  • mathmate
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)?
anonymous
  • anonymous
(5,-5)?
mathmate
  • mathmate
( 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.
mathmate
  • mathmate
Yes, [-5,5] is the correct new range.
anonymous
  • anonymous
So which answer would it be because in f(x) it was [1,-1] to [5,-5] but thats not an option
mathmate
  • mathmate
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.
anonymous
  • anonymous
so it would be a because it went from [1,-1] and shifted down 3 right?
Sachintha
  • Sachintha
It won't be A. Try again. :)
mathmate
  • mathmate
Did you say [-1,1] translated down? Recall we have g(x)=-5cos(x)-3.
mathmate
  • mathmate
We agreed it was [-5,5] before translation, didn't we?
Sachintha
  • Sachintha
@georgia545 Don't look forward for a direct answer. Try to work it out following mathmate's instructions.
anonymous
  • anonymous
i thought it started as [1,-1] in f(x) then went to [5,-5] in g(x) ????
Sachintha
  • Sachintha
The range of function g(x) is [5,-5]. Then it is shifted down 3 units in the negative y direction.
Sachintha
  • Sachintha
Then the range also changes according to it.

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