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8/31 Notes

by: Hanna Markezich

8/31 Notes Math 155

Hanna Markezich
Trigonometry and Elementary Functions

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About this Document

Here is this week's notes. Functions and graphs.
Trigonometry and Elementary Functions
Class Notes
25 ?




Popular in Trigonometry and Elementary Functions

Popular in Mathematics (M)

This 5 page Class Notes was uploaded by Hanna Markezich on Monday August 31, 2015. The Class Notes belongs to Math 155 at Northern Illinois University taught by Vobornik in Fall 2015. Since its upload, it has received 61 views. For similar materials see Trigonometry and Elementary Functions in Mathematics (M) at Northern Illinois University.

Similar to Math 155 at NIU

Popular in Mathematics (M)


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Date Created: 08/31/15
Homework 2 and Quiz 2 due Tuesday 98 by 1159 pm NO CLASS MONDAY Participation hours start this week Need 3 hours in the Mathlab Homework 2 Sections 32 33 amp 35 review 34 at the end of notes along with graphs Sections 32 amp 33 Reading Graphs Definition A function fx is said to be m if fxfx Even functions are symmetric about the yaxis Example fxx2 lt is this even 1 First insert the inverse into the equation iXX2 fxx2 YES Definition A function fx is said to be if fxfx is exact opposite Their graphs are symmetric about the m Example fxx37x lt is this even odd or neither fXX37X x37x lt test take out the inverse x37x fx ODD Example gx2x512 lt even odd or neither gX2X512 2x512 lt test 2x512 NEITHER Now time for graphs NOTE For increasing T decreasing l and constant the answers are ALWAYS open intervals of x values OPEN MEANING NO BRACKETS Function Yes Passes the vertical line test fO3 If fxO what s x X 33 Domain Interval Notation Xvalues look left to right oooo Range a yvalues look bottomup 0 00 Where is the function increasing 32 U 3 oo x values Where is the function decreasing oo 3 U 23 Where is the function constant 22 9 Even odd or neither Even Hint look for symmetry about the yaxis Average Rate of Change Definition average rate of change AROC of a function fx from A to B is 1 2 3 4 5 6 7 8 AROC fBfA lt think slope for functions BA Example Find AROC of fxx23 from 1 A to 5 B f1123 f5523 13 253 2 22 AROC f5f1 51 AROC 222 51 222 24 4 4 6 m We do not cover 34 however I have provided the properties for all 7 functions I encourage to use the video links on Blackboard for review 34 Library of Functions Review 1 fx c Domain 0oo Range 0oo x and y intercept at 00 increasing at 0 00 Neither odd nor even 1 i d E E T 2 oofX V37 Domain and Range oooo x and y intercept at 00 always increasing oooo Odd 3 fx x Domain oooo Range 0 00 x and y intercept at 00 Even 1 4 fxx Domain oooo Range oooo x and y intercept at 00 always increasing Odd 1039 yx din 0113 2quot439039 39339 391390 10 5 fxx2 Domain 0000 Range 000 Increasing 000 Decreasing 00 0 x and y intercept at 00 Even 6 fxx3 Domain 0000 Range 0000 a and y intercept at 00 always increasing 0000 Odd sch le lu flum 13 7 fx Domain 000U 000 Range 000U000 decreasing 00 0U 0 00 no x and y intercepts Odd X Rules for Shifting yfxK shift up by K yfxK shift down by K yfxK shift left by K yfxK shift right by K yfx reflect about yaxis fx reflect about x axis


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