A cubic polynomial function F has zeros

Question

A cubic polynomial function F has zeros of {-3, 0, 2}. Which restriction of the domain of f will allow its inverse to be a function?

A- x > -3

B- X > 0

C- x< 0

D- x> 2

Answer 1

The only way a cubic function can have those three zeros is if 

y = (x+3)(x-0)(x-2)             , multiplied by some constant that we don't care about....

y = x(x+3)(x-2)

y = x(x² - 2x + 3x - 6)

y = x(x² + x - 6)

y = x³ + x² - 6x

The inverse of this is

x = y³ + y² - 6y

 

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Scratch that, I'm not sure if the top stuff will help you.....

If you can, sketch the graph of a cubic function with three zeros and put them at -3, 0 & 2

A. If you can, sketch the inverse graph of this.   It will be the original graph, but reflected across the line y = x

    Do the vertical line test on the intervals given in the multiple choices

B. If you didn't sketch the inverse, you can do a "horizontal line test" on the original graph (note: this is not a legit line test but it still serves the purpose of testing whether the inverses of functions are, themselves, functions)

    This time, you'll do it on the intervals given by the choices but replace x with y

• A. y > -3
• B. y > 0
• C. y < 0
• D. y > 2

 

Either way you slice it, you'll notice that B & C won't work because the graph has points in all four quadrants immediately before 0 and immediately after 0. The interval you need has to avoid all that stuff. And A won't work because it starts at -3, but because it's greater than -3, it still has to go through all that mess near 0 which definitely fails the vertical (or "horizontal") line test.....

Hope this helps,

Frank