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@phi @radar @aloud @AutumnRoseT @xavierbo2 @Data_LG2 @mathmate @HWBUSTER00 @hartnn
i really d know
okay thanks though
@georgia545 @aloud Do you know the range of f(x)?
So the range of y=cos(x) is [-1,1] Are you familiar with the interval notation?
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)?
( 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.