1. a). Calculate (x^5+9x^4-3x^3+5x+8) / (x^2+3x+1) using long division.
b). Write a division statement.
2. Calculate (-2x^4 +x^3-8x^2+11) / (x-6) using synthetic division.
3. Determine the domain, intercepts, asymptotes (if any), and positive/negative intervals. Use these characteristics to sketch the graph of the function on grid paper using pencil and ruler. Then describe where the function is increasing or decreasing. Show all work. Equation: y=2x^2-3/x+3
Please show all work.
I'm sure you can handle the divisions by now. That's just Algebra I or Algebra 2. A few seconds with google will provide you with handy online calculators to check your work.
For the 3rd part, you have
y = (2x^2-3)/(x+3) = 2x-6 + 15/(x+3)
Surely by now you can easily see that this has
vertical asymptote at x = -3
no horizontal asymptote (why?)
zeroes at x = ±√(3/2)
domain is all reals except x = -3
There is a slant asymptote at y = 2x-6
since for large x, the difference between y and this line -- 15/(x+3) reduces to zero.