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Calculus 1, Week 3 Notes

by: Monica Chang

Calculus 1, Week 3 Notes 21-111

Monica Chang

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About this Document

- Functions & models, section 1.1
Calculus 1
Deborah Brandon
Class Notes
25 ?




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This 2 page Class Notes was uploaded by Monica Chang on Sunday September 18, 2016. The Class Notes belongs to 21-111 at Carnegie Mellon University taught by Deborah Brandon in Fall 2016. Since its upload, it has received 12 views. For similar materials see Calculus 1 in Mathematical Sciences at Carnegie Mellon University.

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Popular in Mathematical Sciences


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Date Created: 09/18/16
Week 3 Chapter 1: Functions and Models 1.1  Function – a rule/pattern we determine from data points to predict values where data is missing (each x value has one y value) x→F →F(x) input functionoutput  A function can only be a function if it passes the vertical line test (i.e. each x value has no more than one y value)  A function is one-to-one if it passes the horizontal line test (i.e. each y value does not have more than one x value)  Ex1. Give an equation, domain, and range for this graph: Equation: f(x= {+2,∧x<0 x ,∧x≥0 Domain: (−∞,∞) Range: −∞,−1 )∪¿  Ex2. Sketch a graph and give the domain & range for this equation: f( )=−2− 1√x Graph: Domain: ¿ Range: ¿  Even, Odd, and Neither functions: o Even function: when f (−x)= f (x) o Odd function: when f (−x)=−f (x) o Otherwise it is neither  Increasing vs. Decreasing functions: o A function is increasing on the interval I if f (1) f ( 2henever x 1x 2 in I o A function is decreasing on the interval I if f x > f x whenever x <x in I (1) ( 2 1 2


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