## anonymous 5 years ago 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?

1. anonymous

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?

2. anonymous

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

3. anonymous

Because there are complex solutions.

4. anonymous

Ah, not finding it..

5. anonymous

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

6. anonymous

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

7. anonymous