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Precalculus I

by: John MacGyver

Precalculus I MATH 130

John MacGyver
GPA 3.52


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This 3 page Class Notes was uploaded by John MacGyver on Monday October 26, 2015. The Class Notes belongs to MATH 130 at University of Tennessee - Knoxville taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/229825/math-130-university-of-tennessee-knoxville in Mathematics (M) at University of Tennessee - Knoxville.

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Date Created: 10/26/15
Math I 30 Learning Objectives Chapter 1 Understand and use interval notation and inequalities to describe sets of real numbers Understand and use commutative distributive and associative properties Evaluate real number expressions with exponents radicals and absolute value without a calculator show your work 0 Use scienti c notation 0 Use laws and properties of exponents to simplify expressions 0 Simplify radical and rational expressions 0 39 quot the or J 39 0 Operations with polynomials squaring and cubing and factor including sum and difference of cubes and 4 term polynomials using grouping o Solve equations and inequalities answer using interval notation both by hand show your work give an exact answer and with the use of the graphing calculator give a decimal approximation Example x J2 is an exact answer x N 1414 is a decimal approximate correct to 3 decimal places J2 at 1414 Types linear quadratic know the quadratic formula and how to simplify the answer rational radical absolute value and factorable polynomial Check answers when necessary 0 Express the domain of an expression using interval notation 0 Plot points and find the distance between two points the midpoint the slope and the equation of the line passing through the points 0 Graph simple equations by hand find intercepts and discuss symmetry Know the tests for symmetry 0 Equations of lines know slopeintercept pointslope and general forms Be able to graph the line and find the equation of a line perpendicular or parallel to a given line through a given point Use linear equations to solve simple word problems 0 Circles recognize the equation of circle and put in standard form by completing the square Graph Given information about a circle graph and find the equation Some Rcul quot Study Problems Chapter 1 Review p 131 28 44 58 62 64 76 89 91 99 116 126 Chapter 1 Test p135 17 811721 Math 130 Learning Objectives Fall 07 JFawler Chapter 2 0 Know and understand the de nition of function Be able to recognize a graph or equation which describes y as a function of x 0 Evaluate functions at real numbers and simple algebraic expressions Simplify a difference quotient W for a given function f x Express the domain of a function in interval notation Sketch the complete graph of simple functions by hand Use the graph to find the range of the function Evaluate and sketch the graph of piecewise defined functions Transformations of graphs understand and describe how to use vertical and horizontal shifting re ecting and stretchingshrinking in the correct order to transform the graph of a standard function see page 166 of text for list Graph transformed function by hand Given the graph of a function y f x sketch the graph of its transformation such as y 2f3x 4 or y fx 7 13 or similar expression 0 Combine two functions to make a new function using or composition of functions Give the domain in interval notation 0 Be able to recognize the graph or equation of a function that is onetoone and sketch its graph Restrict the domain of a function to make it onetoone 0 Find the formula and domain and range of the inverse of a onetoone function Chapter 3 0 Graph polynomial functions by hand using transformations of power functions or factoring to find the intercepts Show all intercepts and proper end behavior Graph polynomial functions using the graphing calculator Estimate the coordinates of the xintercepts and local extrema correct to two decimal places Divide polynomials using long division Find the quotient and remainder functions Synthetic division is optional not required on midterms or final exam Given a zero of a polynomial use the factor theorem to factor the polynomial and find all zeros Given the zeros of a polynomial write the formula for the function Sketch the graph of a rational function Find the domain and range all intercepts and the equations of vertical and horizontal asymptotes by hand give exact values and display and label them on the graph Slant asymptotes may appear in homework but will not be on midterms or the final exam Some Rcul quot Studv Problems Chapter 2 Review p 234 32 48 63 68 78 Chapter 2 Test p 235 l 2 4 5 7 9 10 llab Chapter 3 Review p 317 4 17 62 65 67 Chapter 3 Test p 319 l 2 8cd 9acd Math 130 Learning Objectives Fall 07 JFawler Chapt 0 Chapt Some er 4 Sketch the graph of simple exponential and logarithmic functions with transformations Find domain range intercepts and asymptotes by hand and display and label on graph Evaluate logarithmic expressions Give exact values Use Laws and properties of logarithms to expand expressions or combine terms into a single logarithm Solve exponential and logarithmic equations Give exact answers and decimal approximations Show all work Use exponential and logarithmic functions to solve simple word problems er 5 Understand and use the unit circle For any value of t plot the terminal point for t in the proper quadrant and find the reference number Given a terminal point xy for I find the six trigonometric exact values of t Memorize the special exact values of the trigonometric functions p 410 Use them to find exact values for the other three quadrants Know the signs of the trigonometric functions in each quadrant Memorize and use the Fundamental Identities p 414 Sketch one complete period of the graphs of f x sin x and gx cos x and their transformations e g f x asin kx b c by hand Find the amplitude period and phase shift Plot at least five exact points in one period for each graph Given a sine or cosine graph write an equation that represents the curve Find the amplitude period and phase shift Sketch the graphs of y tan x y cot x y sec x y csc x and simple transformations of each Find and display all intercepts and asymptotes find the period quot Study Problems Ill Chapter 4 Review p 383 4 48 60 61 64 Chapter 4 Test p 385 17 6 Chapter 5 Review p 455 6 20 26 36 39 46 Chapter 5 Test p 458 l 7 8 10 Math 130 Learning Objectives Fall 07 JFawler


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