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3.6 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. 0. C.N. 0. 1 st der. test. no extrema. C.N. 0. up. 0. down. Inf. pt. none.

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3.6 A Summary of Curve Sketching

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  1. 3.6 A Summary of Curve Sketching Pay attention or you won’t know which way to turn!

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

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

  4. x = 0 y = 2 Symmetry? none

  5. 0 0 y-int. ( , ) (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

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

  7. C.N.’s .33, -1, 2 -1 .33 2 down down up 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.

  8. x = -1 x = 2 Symmetry? none

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

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

  11. x = 1 Symmetry? none y = x

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