Thread: Graphing Calculator Problem

Hi can someone help me out with this question:

f (x) = 12x^3 - 5x^2 - 11x +6

I have to do the following, and am allowed to use a graphing calculator:

x - intercepts
degree of polynomial
y-int
Domain
Range
Intervals of increase/decrease
Local Minima
Local Maxima
End Behavior


I've done a few of those but for some of them I'm really stuck... can someone spare a few minutes to help me out?

Thanks

If you are using a ti83, ti83+, ti84+, nSpire with ti84+ keypad 1. press y= 2. enter equation for y1 3. x intercepts are the same as roots, so use 2nd trace and press 2 for zero. use left arrow until cursor is below x axis, and press enter. use right arrow until cursor is above x axis and press enter again. Calculator should give you the zeros, which are the x intercepts. Do this 2 more times because polynomial has 3 roots 4. degree of polynomial is the highest power term, or the highest exponent of x. Here, it is 3, so it is 3rd degree 5. Domain. polynomials don't have a restricted domain, so it is from -infinity to infinity 6. range. odd degree polynomials don't have a restricted range, so it is from -infinity to infinity. 7. to find max, use 2nd trace and use max. use arrows to get to the left of a hump, press enter, use right arrow to get to the right of the hump, and press enter. It gives you the relative max. Do the same thing for the min. 8. Since you know the relative mins and maxes, you know where the function increases and decreases. It increases when slope is positive, decreases when slope is negative. 9.For end behavior, look at the graph. It looks like the graph does not have any asymptotes, so the graph is -infinity as you go left, and infinity as you go right. Good luck.