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?

Question

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?

anonymous · Answer

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?

anonymous · Answer

b) the number of ordered pairs with y=0 should equal the # of times it intersects the x-axis

anonymous · Answer

Because there are complex solutions.

anonymous · Answer

Ah, not finding it..

anonymous · Answer

From what I am seeing though; it looks like the y axis hits 0 one time and so does the x axis

anonymous · Answer

$$f(x) =  x^3-3x^2+x-3 = (x-3)(x^2+1)$$
$$f(x) = 0 \iff x=3 \text{ or } x^2 = -1 \implies x = \pm i $$

There are three 'zeros', but the graph only intersects the x axis once because 2 of them are complex.

anonymous · Answer

Thank you for your help

anonymous · Answer

Good work INewton.