[Math] an equation for cosine function graphed below

calculus

enter image description here

my answer ? Please correct me if am wrong and explain your reasoning

$y\,\,\, = \,\,\,5\cos {3 \over 2}\left( {x\,\, + \,\,{\pi \over 3}} \right)\,\, – \,\,2$

Best Answer

You've done it fine... Wolfram says it's right. Shifting rules for graphs is generally employed in such cases. Let $y=f(x)$, then $(y-a)=f(x-b)$ displaces the graph of $y=f(x)$ $a$ units up and $b$ units to the right.

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