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The function
is an odd function with a domain of all real numbers. It has an intercept at the origin
and is always increasing. The function is concave downward for negative
and concave upward for positive
, with an inflection point at
.
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Beyond the Answer
Did you know that the equation
represents a cubic function? This means its graph will have that classic “s-shaped” curve known as a cubic curve. It’s interesting how it can model real-world phenomena, like the flow of certain fluids or even the trajectories of certain spacecraft when analyzing their motion!
When working with cubic functions, a common mistake is to forget about the critical points and inflection points! Make sure to differentiate the function to find where the slope is zero (which corresponds to local maxima and minima) and where the concavity changes. Analyzing these points can help sketch the graph accurately and understand its behavior better!

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