Pre-Calculus

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of f is above or below the x-axis. Determine the y-intercept. Find any symmetries of the graph. Determine the maximum possible number of turning points. Finally, sketch the graph of f. Using a graphing utility to determine any relative maximums and minimums.

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  1. you must have some ideas about some of these topics. At the very least, use a graphing utility to see what the graph looks like, and most of the answers should become clear immediately.

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