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by: Addison Beer


Addison Beer
GPA 3.76

Alexandra Nichifor

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About this Document

Alexandra Nichifor
Study Guide
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This 2 page Study Guide was uploaded by Addison Beer on Wednesday September 9, 2015. The Study Guide belongs to MATH 120 at University of Washington taught by Alexandra Nichifor in Fall. Since its upload, it has received 84 views. For similar materials see /class/192057/math-120-university-of-washington in Mathematics (M) at University of Washington.




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Date Created: 09/09/15
Math 120 Exam II Review Chapters 9 16 The following are some key points from this section of the course However you are expected to know ALL material that we have covered in these chapters Chapter 9 Shifts Dilations amp Reflections 0 Understand the correspondence between changes in the equation for the function and changes in the graph 0 Rules are in the tables on pages 133135 or in your lecture notes 0 Recall that changes to the variable horizontal shiftsdilations are backwards than expected For ex replacing the variable x by 3x ie yf3x compresses the graph horizontally by a factor of 3 0 Review what each operation does to the range or to the domain of the function 0 Order of operations calculator order for operations on the function f and reverse order for operations on the variable x Ex f2x3l2x3l is horiz shift left by 3 then horiz compression by factor of 2 on the graph of fxlxl Alternatively it can be written l2x32l and performed as horiz compression by 2 then horiz shift left by 32 Yet again if we rewrite it as 2lx32l we can think of it as vertical expansion by factor of 2 and horizontal shift left by 32 units Check that all three correspond to the graph of l2x3l Understand how to recognize half circles y k i R2 x h2 and how to relate half circles and quadratics in vertex form to these kinds of operations 0 Understand how to solve equations and inequalities involving multipart functions such as absolute values Chapter 10 Arithmetic of Functions 0 How do you add subtractmultiply divide two functions What is the domain in each case 0 Step Functions 0 You should know how to work with a function that involves more than one multipart function 139 e be able to nd its multipart rule andor graph See the homework in Ch 10 Chapter 11 Inverse Functions Given a graph or an equation in x and y how do you determine whether the function yfx is invertible Given a function you should be able to know the steps to nd the inverse function Understand how to work with functions that are not onetoone such as yx2 How do you nd the domain and the range of the inverse function How do you draw the graph of the inverse if you have the graph of the original function Chapter 12 Rational Functions 0 Be able to nd zeros vertical asymptotes and horizontal asymptotes of a lineartolinear rational function 0 Be able to nd a lineartolinear model from a story problem Chapter 13 Angles Arc Length and Areas ofWedges 0 You should be comfortable working with degree and radian measures of angles and converting from one to another Recall 360 275 rad1 rotation 0 Understand and be able to use the formulas for arc length and area of a wedge Arc length SR9 Where e is the angle subtending the are 5 measured in radians Area of Wedge A12R20 where e is the angle of the wedge measured in radians 0 Review the basic angles Be able to recognize the radian measures for 0 30 60 45 90 180 amp 360 Chapter 14 Circular Motion 0 Angular Speed a change in anglechange in time o the angle 0 swept in t units of time is 0 mt with 0 in rad and m in rad per unit of time o m and 0 are positive if the angle is swept in counterclockwise direction and negative otherwise 0 Know how to convert from RPM to radtime 0 Linear Speed v change in distancechange in time o the arclength s traveled in t units of time is th 0 Formula relating the two kinds of speed VR0 with m in radunit of time 0 You should be comfortable with Belt and Wheel problems Chapter 15 Circular Functions 0 Understand the definition of the trigonometric functions of acute angles in right triangles opposite O Sln 9 hypot henuse ad39acent 0 0059 1 hypot henuse 0 osite o tan9 3 adjacent You should be able to use these functions to answer questions about right triangles in which a side and an angle are known including word problems Understand how to use the unit circle to define these functions for any angle 9 no matter how large positive or negative Recall that o sin6 ycoordinate of P o cos6 xcoordinate of P o tan9 149 slope of line OP where P is the point determined on the unit circle by the terminal ray of the angle 9 placed in standard position Know the trig functions for special angles 0 754 756 753 752 TE etc Given a point P on a circle of radius R with the center at the origin of an xycoordinate system the coordinates of this point are are given by x Rc0s0 y RsinH where 9 is the angle in standard position swept from the positive XaXis to the point P on the circle Most generally Given a point P that moves 0 on a circle of radius R with the center at ch yo 0 with angular speed or radunit of time o and starting at an initial angle 90 from the standard position then the coordinates of P in this coordinate system at time t are are given by x R c0s00 cot xc y R sin00 mt yc Understand how to use tan to nd the slopes of lines with given angles recall 9 is the angle made by the given line with a positive horizontal direction not necessarily the angle given in the problem Chapter 16 Trigonometric Functions continued 0 Be able to sketch the graphs of y sinx y cosx 8L y tan x Know their domains and ranges 0 Understand what a periodical function is and how to determine its period from its graph 0 Know the following key trig identities o sm2xc052x1 recall notation sin2X is shorthand for SlIIX2 O sin x sin sinx is anodd function while cos x COSEGX cosx is an even fat 0 Also know these trig identities o cosx sin x and vice versa 0 sinx and cosX are periodic with period27r so sinx sini39ZEbc i 277k amp cosx cosiZE x i 277k 0 tanx is periodic with period 7 so tanx tanx i 77k Note It is basic but important to realize that trig functions are functions so you should treat them as you would fX For example sinX does not mean sin times X but the function sin evaluated at the angle X Common errors o 8 E why is this INCORRECT o sin3X 3sinX why is this INCORRECT 0 sin X2 sinzx why is this INCORRECT


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