A Summary of Curve Sketching 3.6 A Summary of Curve Sketching Pay attention or you won’t know which way to turn!

none y-int. ( , ) x-int. ( , ) Domain: Asymptote(s) V.A. @ x = 0 H.A. = 2

inc. inc. C.N. 0 1st der. test no extrema C.N. 0 up down Inf. pt. none 2nd der. test f”(0) = undefined no extrema Now let’s graph the given information.

x = 0 y = 2 Symmetry? none

y-int. ( , ) 0 0 (x-2)(x+1) x-int. ( , ) 0 0 Domain: Asymptote(s) V.A. @ x = -1 x = 2 H.A. y = 0 b/c degree of N < degree of D = 0

C.N. -1, 2 (x – 2)(x + 1) dec. -1 2 dec. dec. 1st der. (-1, ) (2, ) -1 2 dec. dec. 1st der. (-1, ) (2, ) no min. or max.’s

C.N.’s .33, -1, 2 -1 .33 2 down up down up Inf. pt.s (-1, ) (.33, ) (2, ) -.15 2nd der. test Use –1 and 2 from 1st der. f”(-1) f”(2) both are undefined, hence, no min’s or max’s Now let’s graph.

x = -1 x = 2 Symmetry? none

(x-2)(x+1) Asymptote(s) V.A. @ x = 1 Slant asym. y-int. ( , ) y = x 0 2 x-int. ( , ) ( , ) 2 0 -1 0 Domain:

C.N. 1 1 inc. inc. 1st der. test = none up 1 down C.N. 1 no inf. pt. f”test at 1 fails

x = 1 Symmetry? none y = x