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# First exam review 15779

UTEP

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This 4 page Study Guide was uploaded by aarellanes3 on Tuesday September 22, 2015. The Study Guide belongs to 15779 at University of Texas at El Paso taught by Victor Hugo Jimenez Nava in Summer 2015. Since its upload, it has received 32 views. For similar materials see Precalculus in Applied Mathematics at University of Texas at El Paso.

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Date Created: 09/22/15

MATH 1508 STUDY GUIDE CHAPTER 1 SECTION 11 RECTANGULAR COORDINATES To understand rectangular coordinates we must understand the number system What this means is we should understand all the sets of numbers used in this math course oz Real Numbers whole numbers gt Example 09 talking about the basics oz Natural NumbersCounting Numbers gt Example All the numbers between in nity and negative in nity Here is where it seems to get triclq kt Rational numbers All the fractions that can be made with whole numbers gt Example23 25 79 45 oz Irrational Numbers Numbers that are not considered rational gt Example n e kt Real Numbers Combination of rational numbers and irrational numbers gt Example3e kt Real lineRepresentation of the number on a number line gt Example Sketch 62049 oz Cartesian plane simply the coordinate plane its used to plot points it has to axes instead of one gt Need to know that the vertical line is yaxis and horizontal line is xaxis Points every point is made up of a pair which translates to x y It39s an odd jump were are going to move into Pythagorean Theorem kt Pythagorean Theorem Is a formula used to nd the missing length of a RIGHT TRIANGLE and only a RIGHT TRIANGLE the side is usually the hypotenuse longest side of the triangle 0 aquot2 bquot2cquot2 gt aquot2bquot2hypotenuse gt hypotenuse xaquot2bquot2 60 In the coordinate plane is made up of points not lengths in other words we need to gure out the distance gt Distance formulaxx2x1quot2y2y1quot2 You get x1 x2 and y1y2 from the points in the graph it doesn39t matter the orderjust keep If they ask you for the midpoint simply add the x1 and x2 then divide by 2 that will be the mid x coordinate then you do the same to the y and that will give you the mid y coordinate simple as pie CHAPTER 1 12 GRAPH OF EQUATIONS oz Equation correlation between to amounts expressed with to variables gt Example n58m the equation is composed of variables quotnquot and quotmquot oz Ordered Pair c d is a solution for the equation when you replace x a yd and it results in the equation being true oz How to sketch a graph of an equation gt Isolate a variable gt Create a table that has solution points gt Plot the points gt Finally connect the points oz Intercepts of a graph To nd where the line crosses the xaxis you must make the equation When y 0 and solve for x vice versa when you look for the y intercept make x0 and solve for y 60 SymmetryGraph of an equation is symmetrical to the xaxis when the parabola is cut in half to make to equal halves along the xaxis in other words y with y both equations equaI each other gt When the graph is symmetric to the yaxis when the parabola is cut in half to make equal halves along the xaxis in other words x with x both equations equaI each other gt When the graph is symmetrical to the origin both x and y get replaced with x andy the parabola gets divided into two equal parts along the yaxis one of the halves though is re ected across the xaxis Equations should still equaI each other CHAPTER 1 SECTION 13LINEAR EQUATION IN TWO VARIABLES 60 It is an equation in the form ymxb msope byintercept gt Example sketch the graph of 3x 5 In this case we have m3 and b5 60 How do we nd the slope of a line Well for that we need two points gt Formula my2y1x2x1 In simple terms rise over run or even simpler they are the change in both axes oz There are two cases a simple one and a complicated one gt Simply is you have all the information know all you need to do is input them into the formula gt The second one is a little more tedious we have slope and a point To nd b use by1mx1 Afterwards use point slope formula yy1mxx1 to gure out the rest 60 Parallel Straight LinesTwo Straight lines gt Ym1xb1 gt Ymx2b2 oz These lines are characterized by same slope gt ExampleWhat equation passes through point 23 and is parallel to the line y43x3 CHAPTER 1 SECTION 14 FUNCTIONS oz Functions model two quantities referred to as phenomena oz Functions are represented by equations oz Domainis all the possible x values or independent values oz Range are all the possible yvalues or all the dependent values oz A piecewise function is a function de ned by parts on 60 VVertical line Testy is a function of x if and only if no vertical line intersects the line at more than one point 60 Finding zeros of a function gt Zeros xintercepts fx0 CHAPTER 1 SECTION 17 TRANSFORMATIONS OF A FUNCTION 60 When you want to know how the graph shifted upwards or downwards simply take into consideration That usually we will notice because the y intercept has changed from the original 60 When there is a shift from left to right or vice versa it has to do with the slope gt Visual representation of vertical changex hxfxc this is upwards subtract when the graph shifts downwards hxfxc shifts to the right c shifts left 60 Re ection basic function yfx gt When you re ect on xaxis hxfx gt When you re ect on yaxis hxfx CHAPTER 1 SECTION 18 COMBINATION OF FUNCTIONS oz Given two functions quotdquot and quotequot we de ne 1 Sum dexdxex 2 Difference dexdxex 3 Product d x edx x ex 4 Quotient dex dxex ex cannot equal zero oz Difference of two squares dquot2 equot2 dede oz Composite functions doexdex 1 d composition with e 60 Decomposing functions ixdexF CHAPTER 1 SECTION 19 INVERSE FUNCTIONS oz Definition let d and e be two functions in order so gt dexx and edxx The domain of d is the range of e The domain of e is the range of d 60 One to One Functions For every value in the x there is no repeats in the y and vice versa 60 Horizontal Line TestIts basically the vertical line test but in this one we test if it39s a one to one function 60 Theorem One to one functions can only have an inverse not any other type of function CHAPTER 2 SECTION 21 QUADRATIC FUNCTIONS oz axquot2bxc a b and c are real numbers except a cannot equal 0

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