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# Difcalc10week2

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Esta es la presentación de las sesiones de la semana 2 de mi curso de Cálculo diferencial en el pizarrón electrónico.

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### Difcalc10week2

1. 1. Opener. True or False: 1. A function is a set of ordered pairs. 2. A function is a set of ordered pairs where the ﬁrst element of each ordered pair is never repeated.
2. 2. Are the following graphs of relations? Are they graphs of functions? Sweep a vertical line across the graph of the function. If the line crosses the graph more than once it is not a function, only a relation.
3. 3. Relations Functions
4. 4. Domain and Range. Domain. Is the set of "input" or argument values for which the function is deﬁned.
5. 5. Domain and Range. Range. Refers to the output of a function.
6. 6. State the domain and range of the following functions. Domain: Domain: Range: Range:
7. 7. State the domain and range of
8. 8. Homework. Posted on Blackboard (Assignments).
9. 9. Lines. Opener. 1. What is the slope of a line? 2. Write the general equation of a line. 3. Given the general equation of a line, how would you ﬁnd its slope?
10. 10. Things you should always remember: 1. Given two points (x1, y1) and (x2, y2): General Equation: Slope-intercept Equation: Point-slope Equation: Parallel Lines: Perpendicular Lines:
11. 11. Exercises. Working in pairs, solve problems 9, 10, 12, 13, 14, 23, 25, 27, 41, 43, 45, and 47. To hand in at the end of the session. Homework. Posted on Blackboard (Assignments).
12. 12. Rational functions. Opener. 1. What is a rational function? A function that can be expressed as a quotient of polynomials, excluding division by zero. 2. Consider . What is the domain? And for ? 3. What is an asymptote? A line that a graph gets closer and closer to, but never touches or crosses it.
13. 13. Guidelines for Sketching the Graph of a Rational Function. Guideline 1 Guideline 2
14. 14. Guidelines for Sketching the Graph of a Rational Function. Guideline 3 Guideline 4
15. 15. Guidelines for Sketching the Graph of a Rational Function. Guideline 5 Guideline 6
16. 16. Exercises. Sketch the graphs of the following functions.
17. 17. Homework. Posted on Blackboard (Assignments).
18. 18. Class Activity: Sine and Cosine functions.
19. 19. Sketch the graph of the following functions.
20. 20. Quiz.