Final Exam Study Guide- 011-01 Dynamics of Algebra Chapter Section Example Chapter What is a function? Properties of a function Is it a function? Explain. Finding the Slope Slope y y m = x x 1 1 Find the slope between two points: (-,) and (4,-8) Writing the Equation of a Line Writing the equation given a word problem A businessman earns a salary of $0 per week and an additional 10% in commission of his sales, c. Write an equation to model the amount of money, s, the businessman earns per week. Write the equation of a line given a point and a slope. y = mx+ b m = ; (,1) Write the equation of a line given a point and a line parallel or perpendicular. - Parallel same slope - Perpendicular opposite reciprocals (flip it and switch it) Point: (,1) Line parallel to y = 5x+ 5 Point: (,1) Line perpendicular to 1 y = x+ 5
Write the equation of a line given a graph. Absolute Value Equations Find the vertex. y = a x h + k Vertex :( h, k) Slope : a y= x 5 + Vertex : Chapter Solving a system of Equations - Substitution o Solve for the lonely variable. - Elimination o Pick a variable, get same number, different signs. - Graphing o Intersection of two lines is your answer. o Word problems like the cell phone project (which is better plan and when?) Cases: - One Solution: Intersecting Lines - Infinitely many solutions: Coinciding Lines - No Solution: Parallel Lines Word Problems 4x 6y = 1 x+ y = 6 The senior classes at High School A and High School B planned separate trips to the county fair. The senior class at High School A rented and filled 11 vans and 6 buses with 510 students. High School B rented and filled 5 vans and buses with 194 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Linear Inequalities - Slope intercept form - Standard form Get into slope-intercept form >,< : dotted, : solid y< x y x+ Chapter 5 Different Forms Vertex form: y= a( x h) + k Standard form: y= ax + bx+ c Intercept form: y= a( x p)( x q) y= x+ 1 1 in? What form is ( ) What form is y x x = + 5 1in? What form is y ( x )( x 4) = + in? Graphing Roles of a, h, k a : shaper, up/down, wide/narrow h : horizontal shift k : vertical shift Describe the graph using a,h, and k. ( x ) y= + 1 1
Graph y= x+ 1 1 Graph: ( ) 1. Find the vertex.. Graph using the a-table a = 1a 1(-) - Right one, down a (-) -6 Right one, down 6 5a 5(-) -10 Right one, down 10 Graph: y= x x+ 4 1 Find the vertex: Vertex form ( hk, ) Standard form b Vertex : x = a plug in to equation to solve for y Find the vertex: ( x ) y= + + 1 y= x x+ 4 1
Vertex standard form - Open up the present - FOIL ( x ) y= 1 + Converting Intercept standard form - FOIL ( )( ) y = x 1 x 4 Relating a graph to zeros (x Intercepts) Estimate the real zeros of the function graphed below. Round to the nearest whole number. Graphs of Zeros Number of solutions and intercepts - 1 real solution 1 x-intercept - real solutions x -intercepts - No real solutions 0 x -intercepts Sketch a graph with one solution. Sketch a graph with zero solutions. Sketch a graph with two solutions.
Old School/Difference of squares Factor: x + 1x+ x 64 Factoring 4x 5 Solving quadratic equations What are the solutions/x-intercepts to the equation? x 11x+ 10= 0 Radicals - Simplify 4 18 Solve for the x-intercepts using radicals. x + 10= 90 Quadratic Formula ± x = b b 4ac a Find the zeros. x + 4x = 0 Solving quadratic equations for x intercepts
Chapter 6 Exponents Exponents ( 4x ) - simplifying xz y 0 4 Adding/subtracting Add/Subtract and write in standard form: ( x 4x+ ) + ( x 4 + x) (x + 4x+ ) ( x 4 + x) Polynomials Dividing using synthetic division (x + 4x x+ ) ( x 1) Graphing End Behavior Sketch the graph of the equation: y= x + x x+ 4 Describe the end behavior: as x + as x Describe the end behavior: as x + as x x + means as you move to the right x means as you move to the left f(x) means the graph 4 y= x + 4x + Describe the end behavior: as x + as x
Vocabulary - Leading Coefficient - Degree - Constant Name the leading coefficient, degree, and constant of the polynomial shown below: x + 4x x+ Chapter 7 Exponential Radical Notation with coefficients /4 x Radical Notation Exponential ( ) 4 x Find the inverse y = x Composition of functions f( x) = x+ 1 gx ( ) = x+ 1 Simplify f ( g() x ) Rational Exponents Simplify g( f() x ) Solving radical equations x 1 = x x + 1=
Chapter 8 Evaluate log4 64 Converting - exponential log - log exponential 5 Convert to logarithmic: = Convert to exponential: log 9 = Logs Condense Write as a single logarithmic expression: log x log y Expand Expand: log xy z Exponential Functions Word Problems Classify as Exponential Decay/Growth and identify the growth factor. t A= a( 1+ r) Growth = ( ) 4 t ( 1 ) A= a r Exponential Growth Exponential Decay Decay = Compounded Interest n= quarterly = monthly = weekly = daily= Continuously Compounded Interest 4 Classify as Exponential Decay/Growth. 1 x y = t ( 1 ) t ( 1 ) A= a + r A= a r r A= P 1+ n A= Pe rt nt