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## CURVE SKETCHING TEST  a. x 0
b. x -1,1
c. x 1
d. x -0.25,0.25 a.x-intercept: x = -1,1, y-intercept:  y = 0
b.x-intercept: x = 0, y-intercept:  y = 1
c.x-intercept: x = -3,3, y-intercept:  y = 1
d.x-intercept: x = 0, y-intercept:  y = 0 a. symmetric about x-axis (even function)
b. symmetric about origin (odd function)
c. periodic function
d. no symmetry a. horizontal asymptote: y = 0, vertical asymptotes: x = -1,1
b. vertical asymptotes: x = -1,1
c. horizontal asymptote: y = 1, slant asymptote: y = x3
d. horizontal asymptote: y = 0, vertical asymptotes: x = -0.25,0.25 a. decreasing on (- , )
b. decreasing on (- ,-1), (0,1), increasing on (-1,0), (0, )
c. decreasing on (- ,-1), (-1,1), (1, )
d. decreasing on (-1,0), (0, ), increasing on (- ,-1), (0,1) a. local maxima at x = -1,1, local minimum at x = 0
b. local maximum at x = 0, local minima at x = 1,1
c. local maximum at x = -1, local minimum at x = 1
d. no local maxima or minima a. concave down on (- , )
b. concave up on (0, ), concave down on (- ,0)
c. concave up on (-1,0), (1, ), concave down on (- ,-1), (0,1)
d. concave down on (- ,-1), (-1,1), (1, ) a. inflection point at x = 0
b. inflection points at x = -1,0,1
c. inflection points at x = -1,1
d. no inflection points a. b. c. d. If you had any trouble with this advanced test, it is strongly recommended that you review the content of the Curve Sketching Tutorial before attempting to take this test again. It is also recommended that you complete the General Curve Sketching Test on the iLrn website and the questions from the Curve Sketching Sample Problems page. The links for all of these resources can be found below.

Curve Sketching Tutorial
Curve Sketching Problems
General Curve Sketching Test on iLrn

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COURSE HOMEPAGES
MATH 1036
MATH 1037

FACULTY HOMEPAGES
Alex Karassev
Ted Chase