Given the function f(x)=x^3-3x^2+x-3 Discuss: a) How many times does intersect the x-axis? b) Compare the number of zeros and the number of times it intersects the x-axis. Why the difference?

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Given the function f(x)=x^3-3x^2+x-3 Discuss: a) How many times does intersect the x-axis? b) Compare the number of zeros and the number of times it intersects the x-axis. Why the difference?

Mathematics
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set the function equal to zero. likewise you can plug the function into your calculator under the y= menu and go 2ND->Graph and look at the table, wherever y=0 that's where it intersects the x-axis. b) not sure if i understand the question, the number of zeros?
b) the number of ordered pairs with y=0 should equal the # of times it intersects the x-axis
Because there are complex solutions.

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Ah, not finding it..
From what I am seeing though; it looks like the y axis hits 0 one time and so does the x axis
\[f(x) = x^3-3x^2+x-3 = (x-3)(x^2+1)\] \[f(x) = 0 \iff x=3 \text{ or } x^2 = -1 \implies x = \pm i \] There are three 'zeros', but the graph only intersects the x axis once because 2 of them are complex.
Thank you for your help
Good work INewton.

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