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by: Monica Chang

23

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# Calculus 1, Week 5 Notes 21-111

Monica Chang
CMU

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- power functions - polynomial functions - trigonometric functions - exponential functions - logarithmic functions
COURSE
Calculus 1
PROF.
Deborah Brandon
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Mathematical Sciences

This 2 page Class Notes was uploaded by Monica Chang on Saturday October 1, 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 23 views. For similar materials see Calculus 1 in Mathematical Sciences at Carnegie Mellon University.

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Date Created: 10/01/16
Power Function:  In the form y=a xb 2 4 4 2  Comparing the graphs of x and x , x is flatter than x when x is between -1 and 1 and steeper for the rest of the domain.  Comparing the graphs of x and x , x is flatter than x 3 when x is between -1 and 1 and steeper for the rest of the domain.  Any even root like √x is neither odd nor even because its domain doesn’t even include –x 1  Any reciprocal of an even root like √ x is even because f (−x)= f (x) 3  Any odd root like √ x is an odd function because f (−x)=−f (x) 1  Any reciprocal of an odd function like 3 is odd √x because f (−x)=−f (x) Polynomials:  In the form: y = a · n + an n −1· xn −1+ … + a · x 1 a 0  The degree of a polynomials is the exponent of its largest exponent term.  The sign of the highest order term will tell you the overall direction of the graph.  If for some value x=p , f (p)=0 , we know that x−p f (x) must be a factor of the function .  Rational Functions: P(x) o fx)= where P and Q are polynomials Q(x) o D (f={x∈R , Q(x)≠0 }  Algebraic Functions: o Quotient of “polynomials” where powers can be any real # o Rational functions & polynomial functions are algebraic, but not all algebraic function are rational or polynomial Trigonometric Functions:  In the form: y = a sin (b x + c)  You can use graphs of sin and cos to help with values at different annles.  Cosθ) =cos θ  Sinθ)=sin θ 2 2  Sin θ+Cos θ=1  S∈(−x =−sin x becausesinisan odd function  C o(−x =cos x)becausecosisaneven function o Example: C o(−3x+6π ) ¿cos−3x ) ¿cos(3x) Exponential Function: x  In the form: y=a ,a>0  D(f)=(−∞ ,∞ )  R(f)=(0,∞)  b plug∈time x¿ get measureof growth  lob x plug∈growth¿getmeasureof time Logarithmic Function:  In the form: y=log a  D(f)=(0,∞)  R(f)=(−∞,∞ )

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