MAC 1105 MAC 1105-88394
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This 3 page Bundle was uploaded by Alicia Rooney on Sunday September 18, 2016. The Bundle belongs to MAC 1105-88394 at Hillsborough Community College taught by Mrs. Duncan in Fall 2016. Since its upload, it has received 11 views. For similar materials see College Algebra 1105 in Mathematics at Hillsborough Community College.
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Date Created: 09/18/16
MAC Exam 1 Sections 1.4-2.2 1.4: o Complex Numbers Standard from A+Bi Watch the signs Remember to distribute the negative sign in the case of (a+bi)-(a-bi) i = -1 Square root of -1=i 1.5: o Quadratic Equations Methods- factoring, square rooting, and completing the square Factoring o EX: x -4x-5 (x+1)(x-5) Square rooting o X -16=0 x =16 Take the square root of both sides Remember to use plus or minus when square rooting o X= plus or minus 4 Completing the square o X -10x+2=0 X -10x=-2 From here you would divide B (10x) by 2 (5) and then square that (25) X -10x+25=-2+25 2 X -10x+25=23 Then factor the left side, and from there square root both sides and solve for x 1.6: o Other Types of Equations Polynomials and absolute value Polynomials (in the prep test there are not any problems like this so I will just write out what to do) Set the polynomials equal to zero Then group them into two parts Find the GCF for each portion, what’s left in the parenthesis should equal each other Put the GCF in another parenthesis multiplying what was left in the other parenthesis from the step before Set the equation equal to zero Factor more, if needed Solve for each X separately Absolute Value Distance from zero When given an absolute value, make sure that it is by itself, add/subtract and/or multiply/divide to the other side Then have two different equations, one where the contact is positive and the other negative o EX: 3x-5=10 and 3x-5=-10 Then solve for X 1.7: o Inequalities The solutions of |u|<C are the numbers that satisfy – C<U<C The solutions of |u|>C are the numbers that satisfy U<-C or U>C when the inequality sign is facing the functions there will be two equations that need to be solved, the original and one where the inequality sign is flipped and the sign is changed of C use the union symbol (U) when writing in interval notation for these Interval notation: [-1,3] 2.2: o Function and Graphs 2 Many solutions One solution involves two numbers for X and Y Ordered pairs are solutions Store solutions in a T table For ever X there can only be one Y To check if a graph is a function do the vertical line test, there are not two spots for one X Solve for Y and determine if only one result is obtained F(X)=Y EX: F(4) plug in 4 for every X in the equation to solve for Y Domain is all the X’s Range is all the Y’s 2.2 o More on Functions Even functions- y-axis symmetry, f(-x) = f(x) Odd function- point symmetry, goes through origin, f(-x) =-f(x) Neither- no symmetry Relative maximum- the highest “neighborhood” Relative minimum- the lowest “neighborhood” Absolute maximum/minimum- the absolute lowest/highest “neighborhood” Equation to know: f(x+h)-f(x) all divided by h For piece wise functions look at the sign and the number that the X can or cannot be 3
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