A Summary of Curve Sketching - Oregon High...
Transcript of A Summary of Curve Sketching - Oregon High...
![Page 1: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/1.jpg)
1
3.6 A Summary of Curve Sketching
Vertical asymptotes (Section 1.5)
xintercepts and yintercepts (Section P.1)Symmetry (Section P.1)
Domain and Range (Section P.3)Continuity (Section 1.4)
Differentiability (Section 2.1)Relative extrema (Section 3.1)
Concavity (Section 3.4)Points of Inflection (Section 3.4)
Horizontal asymptotes (Section 3.5)Infinite limits at infinity (Section 3.5)
Tools/Concepts useful in Sketching a Graph[p202]
![Page 2: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/2.jpg)
2
1. Determine the domain and range of the function.2. Determine the intercepts, asymptotes, and symmetry of the graph.3. Locate the xvalues for which f '(x) and f "(x) are either zero or do not exist. Use the results to determine relative extrema and points of inflection.
NOTE: In these guidelines, note the importance of algebra (as well as calculus) for solving the equations f (x) = 0 , f '(x) = 0 , and f "(x) = 0 .
Guidelines for Analyzing the Graph of a Function [p 202]
Polynomial Functions
Rational Functions f (x) = p(x)h(x)
if the degree of p(x) exceeds the degree of h(x) by one, oblique (slant) asymptote (after long division)
Radical Functions f (x) = xn
Trigonometric Functionsomit
![Page 3: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/3.jpg)
3
examples: Analyze and Sketch. [p208 #26]1. y = (x3 3x + 2)1
3
![Page 4: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/4.jpg)
4
1.y y' y" Conclusion
![Page 5: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/5.jpg)
5
examples: Analyze and Sketch. [p208 #16]
2. f (x) = x3x2 4
![Page 6: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/6.jpg)
6
2.
![Page 7: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/7.jpg)
7
2.f (x) Conclusionf '(x) f "(x)
![Page 8: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/8.jpg)
8
examples: Analyze and Sketch. [p208 #20]
3. g (x) = x 9 x
![Page 9: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/9.jpg)
9
3.
![Page 10: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/10.jpg)
10
3.
g (x) Conclusiong'(x) g"(x)
![Page 11: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/11.jpg)
11
examples: Analyze and Sketch.
4. f (x) = 2x 5x 53 43
![Page 12: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/12.jpg)
12
4.
![Page 13: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/13.jpg)
13
4.
f (x) Conclusionf '(x) f "(x)
![Page 14: A Summary of Curve Sketching - Oregon High Schoolteachers.oregon.k12.wi.us/debroux/Calc/3.6lessonkey(3 days).pdf · 1 3.6 A Summary of Curve Sketching Vertical asymptotes (Section](https://reader033.fdocuments.in/reader033/viewer/2022052408/5f094dd77e708231d4263035/html5/thumbnails/14.jpg)
14
p208 #16, 25, 31, 35 7, 9, 11, 17 19, 21, 23, 5258
Assignment:polynomial
rational
radical concepts
matching ; reasoning