Curve Sketching

1. Curve Sketching section 3-A continued

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

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

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

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

7. Home Work Page 195 # 21, 24, 25, 36, 41, 48, and 49 worksheet 3-A