MATH Lecture 16 February 24,2017

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Muriel Cummings
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1 MATH 101 Lecture 16 February

2 Announcements HW # due in class Monday Feb 27 : time Quiz # 3 Tuesday February 28 Sections Read 2Section for next Multiple Choice questions today!

3 2.4 Library of Functions & Piecewise Functions

4 intercept Ex x ) X f ( ) f ( = ) C =3 :f( Q : What is the y of fix )? A) C B) 0 C) None D) Don't Know

5 intercept intercept f ( x ) = C The constant function fk)=c Ex : fk ) = 4 Ex : fk ) = 1 Domain : R aka to a) Range : { C } Even function because fk ) = ffx ) = C. Constant on interval to a). y : C X : none ( unless c=o )

6 f ( ) = X f ( ) = X f ( ) Q : On what interval is fk ) increasing? A) 0 ) B) None C) to a) D)?

7 intercept fk f ( ) = X The identity function fk )= 3 e. ( 00 ) 3 ( 22) Domain : R aka to as ) Range : R aka to a) Odd function because ffx ) = = ) Increasing on f a) y :O X intercept : O

8 fk )= 2 f ( ) = X f ( ) Q : What is the range of f ( x )? A) R B) ( 0 a) c) Xto D)?

9 intercept flx )= 2 The Square function f(x)= 2 n t.h.io?m ' 's Domain : R aka to ) Range : ( 00 ) Even function because ftx ) = 2= f ( ) Decreasing on to o) Increasing on ( o as ) y :O X intercept : 0

10 = f ( ). 3 f ( ) = X f ( ) Q : What Is the domain of f ( )? A) X 70 B) Xt 0 C) R D)?

11 intercept fk f ( ) = 3 4 µ The cube function f ( = ) 3 11) H 4 Domain : R aka to os) Range : R aka to A) Odd function because ffx ) = ) 3= Increasing on fos a) y :O X intercept : 0

12 f ( ) = VX f ( ) = X f ( ) Q : On what interval is fk ) decreasing? A) too o ) B) ( 0 a) C) None D)?

13 intercept 4) The square fcx )= root function fk)=rx ( 42 ) #notice : looks but y=x2. like graph of only Domain : ( 0 a) Range : ( 00 ) sideways half Neither even nor odd : fl 4) =2 but FC. is undefined. y Increasing on ( o as ) :O X intercept :O

14 f ( x ) = FX f ( ) = X f ( ) Q : What is the domain of ftp. A) X > 0 B) R C) ( o a) D)?

15 intercept fk fcx ) = FX The cube root function f( )= Fx 8 C 2 ) ( 11 ) # Domain : R aka to os) Range : R aka to oh Odd function because ffx ) = ) F = Increasing on f a) y :O intercept : O

16 f ( ) = t f ( ) = X f ( ) Qi On what is fk interval ) decreasing? A) too o ) U ( 0 a) B) R C) ( 0 a) D)?

17 intercept. a fk f ( The reciprocal function )= t fk)=k 3 3 i Domain 0)Utx = Kitty o)u( 00 ) Range : to o ) U ( 00 ). 3. } :C Odd function because ffx ) = y Decreasing onto : none X ( 00 ) intercept : none )

18 f ( D= 1 1 f ( ) = X f ( ) Q : Is f ( ) A) Even B) Odd C) Both D) Neither

19 intercept f ( D= 1 1 The absolute value function flx )= 1 1 (3.3 ) ; 22 ) Domain : R aka Range : ( 00 ) Even function because ftx = = ) 1 1 :O X intercept : O f ( x ) Decreasing on to o) Increasing on ( o as ) y

20 f ( x ) = int ( x ) The greatest integer function int ( x ) int K ) is the greatest integer less than x. f ( ) = X f ( ) Q : What is the of f ( x )? range

21 intercept fcx ) = int ( x ) The greatest integer function int ( x ) intk ) is the greatest integer less than x. E. g.int ( 3.2 ) =3. int ( 1. ) = 2 dl 0 a * o a Domain : R aka to ) Range : The integers Neither even nor odd. y Constant on the interval [ n nh ) for any integer :O x intercept : all Values in [ 0 D n

22 Continuous Functions Can draw the lifting the pencil graph no gaps in one stroke without or holes Continuous discontinuous ~ a n n n r

23 Piecewise Defined Functions Different Equations for different values of X. Ex : fat ' { 8<2%2 x if 2 +6 if 11>2

24 Piecewise Defined Functions Different Equations for different values of X. Ex : f( )= 2 if XEO a { if 0< XE 2 b 2 +6 if 11>2 C =4

25 1) Piecewise Defined Functions Different Equations for different values of X. ff f ( end :O 2) Ex : f( )= " 2 if XEO a { if 0< XE 2 b 2 +6 if 11>2 C.= Ts= =L =4

26 Piecewise Defined Functions Different Equations for different values of X. Ex : f( )= 2 if XEO a { if 0< XE 2 b 2 +6 if 11>2 C =2=4 " onion fl 1) =1 f (a)

27 Piecewise Defined Functions Different Equations for different values of X. 2 if a XEO Ex : f( )= { if 0<XE2 b one a)! 2 +6 if 11>2 C.=b s= = f( 2) :# fl 3) = 21 3) +6 = 0

28 Piecewise Defined Functions Different Equations for different values of X. Ex : f( )= 2 if XEO a { if 0<XE2 b 2 +6 if 11>2 C.=Tcj Q : Is f ( ) % continuous?.

29 Piecewise Defined Functions Different Equations for different values of X. 2 if a XEO Ex : f( )= { if 0< XE 2 b 2 +6 if 11>2 C

Sect 2.6 Graphs of Basic Functions

Sect 2.6 Graphs of Basic Functions Sect. Graphs of Basic Functions Objective : Understanding Continuity. Continuity is an extremely important idea in mathematics. When we say that a function is continuous, it means that its graph has no