C URVE S KETCHING section 3-A continued

Analyzing the graph of a function a)Domain and Range: All real numbers except ___ b)Extrema and the intervals where increasing and decreasing (first derivative test) c)Intercepts: where the graph crosses the x-axis and the y-axis d)Inflection points and the intervals where concave up and concave down (second derivative test) e)Symmetry 1.About the y-axis if even function 2.About the origin if odd function

Find all critical values f) Asymptotes- rational functions Vertical: set the denominator equal to zero and verify the limit tends to infinity Horizontal: Take the limit of the function as x approaches ±∞ Slant: occur when the degree of the numerator is one higher than the degree of the denominator. Use long division or synthetic division to find the line g) Graph- put it all together

4) Analyze the graph (parts a through g) then sketch a)Domain and Range b)Extrema and the intervals where increasing and decreasing (first derivative test) c)Intercepts: where the graph crosses the x- axis and the y-axis d)Asymptotes- vertical, horizontal and slant e)Inflection points and the intervals where concave up and concave down (second derivative test) f)Symmetry g)Graph- put it all together

5) Find the intervals where concave up and concave down if

6) Analyze the graph (parts a through g) then sketch

H OME W ORK Page 195 # 21, 24, 25, 36, 41, 48, and 49 worksheet 3-A