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# College Algebra Lab MAT 107

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This 33 page Class Notes was uploaded by Mrs. Elliott Bartell on Sunday October 11, 2015. The Class Notes belongs to MAT 107 at Eastern Kentucky University taught by Robert Buskirk in Fall. Since its upload, it has received 21 views. For similar materials see /class/221452/mat-107-eastern-kentucky-university in Mat Mathematics at Eastern Kentucky University.

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Date Created: 10/11/15

Section 24 Complex Numbers R D Buskirk Eastern Kentucky University Fall 2008 Goals You will learnreview 0 basic properties of the number 239 x 1 imaginary unit 0 complex numbers real part imaginary part standard form ax 9239 0 basic arithmetic with the complex numbers additionsubtraction multiplicationdivision o conjugate denoted a 9239 a 9239 of a complex number a bi 0 use other vocabulary such as imaginary unit complex number imaginary number pure imaginary number real number natural number integer rational number irrational number Practice Problems Problem 1 Check all of the following that apply z 1 xS 5 0 01 imaginary unit complex number imaginary number pure imaginary number real number natural number integer rational number irrational number Problem 2 Perform the indicated operations and write the answer in simpli ed standard form a 2395 21003 c 32 d 4 5239 8 3239 e 2 502 f 2 502 5239 g 3 4 1 2 3239 h 1 1 3239 2 3239 Problem 3 Solve for the indicated variables forxandy 2 1 a 3x z 42y11 b 3 iz2if0rz 01 Problem 4 Perform the indicated operation and write the answer in standard form a 9239 cdi Section 21 Linear Functions R D Buskirk Eastern Kentucky University Fall 2008 Goals You will learn review 0 how to compute the rise run or slope of a line segment and interpret its meaning geometrically 0 how to nd the intercepts of a line and interpret its meaning geometrically 0 how to graph lines given two points a point and the slope and equation 0 how to nd the equation of a line using pointslope form y yl mx x1 slopeintercept form y mac b standard form aka generalform Ax By C A Z 0 There is also a special intercept form that makes it easy to see both intercepts E g 1 04 0 geometric and algebraic properties of parallel and perpendicular lines 0 how to do all of the above for vertical lines 0 other terms like unde ned slope linear equation slope of secant line slope of tangent line average rate of change Practice Problems Problem 1 Use the graph of the linear function to nd a rise a run and the slope Write the equation of the line in standard form Problem 2 Use the graph in the previous problem a Approximate the intercepts of the linear function b nd the intercepts of the linear function algebraically Express the solutions exactly Problem 3 Which of the following de ne a linear function IE 3 a y 12 y3 b2 x 1 0 my 3 1317T2 y Jc 17 e 11quot 17 12 Problem 4 Write the equation of the vertical line that passes through the point 617 Problem 5 Write the equation of the line that passes through the points 3 2 and 8 1 in standard form Problem 6 Write the equation of the line that has slope and goes through the point 3 2 in slopeintercept form 01 Problem 7 Write the equation of the line that has xintercept 3 and yintercept 5 in slopeintercept form Problem 8 Write the equation of the horizontal line that passes through 18 17 the point 3 H in slopeintercept form Zl Problem 9 Find the equation of the line L2 that passes through the point 3 2 and is parallel to the line L1 2x 3y 6 Graph both lines below 51 Problem 10 Find the equation of the line L2 that passes through the point 3 2 and is perpendicular to the line L1 2x 3y 6 Graph both lines below 171 Problem 11 Let f 1162 Find the equation of the secant line 3 3 connectmg the pomts 0n the graph at x 1 and x 5 SI Work problems 84 and 88 Section 27 Solving Inequalities R D Buskirk Eastern Kentucky University Fall 2008 Goals You will learn review to o understand inequalities analytically with symbolic expressions graphically and verbally o solve linear inequalities o solve absolutevalue inequalities o solve quadratic inequalities o solve combined inequalities 0 use inequalities for mathematical modeling Practice Problems Problem 1 Use the graph below to answer the following Approximate to the nearest 01 unit Write answers in both interval and inequality notation a x 2 0 b it S 90 0 f969 gt 0 Problem 2 Write as an inequality u is more than 5 units from 1 Graph the solution set express the solution set in interval and inequality notation different from the original inequality Problem 3 Solve each inequality Express the solution using set notation interval notation and a graph a x 5lt 4 7 2x23 5 4 7xlt17 Problem 4 PM 7T E 5lt3 2 2 1 2xgt 3 Section 25 Quadratic Equations and Models R D Buskirk Eastern Kentucky University Fall 2008

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