Subjects algebra

Transformed Cubic 728427

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1. The problem asks to find the equation of a cubic function transformed so that its inflection point is at $(-3,-2)$ and the graph increases from bottom-left to top-right. 2. The basic cubic function is $y = x^3$, which has an inflection point at the origin $(0,0)$. 3. To move the inflection point to $(-3,-2)$, we apply a horizontal shift by $+3$ and a vertical shift by $-2$. 4. The transformed function is therefore: $$y = (x + 3)^3 - 2$$ 5. This function retains the cubic shape and the inflection point is now at $(-3,-2)$ as required. 6. The graph increases from bottom-left to top-right because the leading coefficient is positive.