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We want to get $h(x)= 0.29\cos(3x+4.2)$

$ y = \cos x$ -> multiply $x$-axis 0,29 -> $y=0.29\cos x$ -> multiply $y$-axis $1/3$ -> $y=0.29\cos(3x)$ -> translation $(-1,4;0)$ -> $h(x) = 0.29\cos(3x+4.2)$

Is this correct? I know you can more easily translate first, however I like to use as a rule of thumb to always multiply before translating.

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The $0.29$ has the effect of shrinking in the vertical ($y$-axis) direction. The reason for that should become apparent if you think about plotting points. Similarly, the $3$ shrinks in the $x$-direction.

You really should learn why these things work the way they do by thinking about graphs. That way, if you forget how it works, you'll know how to figure it out.

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Thank you kind sir, but that was not my question. My question was whether my answer is correct or not – ylykcoitus Sep 16 '12 at 18:14
@ylykcoitus : I think my answer should make it clear that yours is not correct. – Michael Hardy Sep 17 '12 at 16:27

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