Key to Practice Midterm III

Problem 1

A.  No Positive roots, 5, 3, or 1 negative root.

B.  -1, -1/2

C.  Roots:  -1, -1/2;    (x + 1)²(x² + 1)(2x + 1)

D.  Left down, Right up

E.  at x = -1:  Concave down parabola.  at x = -1/2:  line

F.  (0,1)

Problem 2

A.  Oblique asy at y = x - 6:  does not cross this asymptote;  Hole at (1,1);  x-int (2,0) and (3,0);  y-int (0,6)

B.  VA:  x = 1;  HA:  y = 0;  no holes;  crosses the asymptote at (0,0);  x-int:  (0,0)  y-int:  (0,0)

Problem 3

(-infinity,1.2) u (3.3,infinity)

Problem 4

A.  7

B.  20

Problem 5

1/2 x²(x² + 16)(x² - 6x + 7)