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# Download Algebra III/Trigonometry Honors Final Exam Study Guide Ch 2

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Algebra III/Trigonometry Honors Final Exam Study Guide Ch 2: Functions Graph piecewise functions Evaluate functions, add, subtract , multiply, and divide functions Find the domain and range of functions Find the inverse of a function and the restricted domain Find the difference quotient Find the intervals where a function is increasing, decreasing, or constant Solve word problems involving linear functions Graph functions using transformations Ch 3: Polynomial Functions Graph polynomial functions including cubic functions Find the zeros of a polynomial functions Use the rational root theorem to find all possible rational roots of a polynomial function. Ch 4: (sections 4.1, 4.2) Rational Functions Graph rational functions Identify any asymptotes (horizontal, vertical, slant) Find the domain and range of rational functions Ch 5: Exponential and Logarithmic Functions Graph exponential and logarithmic functions and give the equations of the asymptotes Write logarithmic equations in exponential form and vice versus Expand and Condense logarithmic expressions Solve exponential and logarithmic equations Find the domain and range of exponential and logarithmic functions Solve word problems involving exponential equations Ch 6 Trigonometry Determine the trigonometric functions given a point on the terminal side of the angle Solve word problems with trigonometric equations Graph trigonometric functions Solve trigonometric equations Find the six trigonometric functions given an angle on the unit circle Convert angles from degrees to radians and vice versus Convert angles from degrees, minutes, seconds to decimal degrees and vice versus Ch 7 Trigonometric Identities Verify trigonometric identities Determine the other 5 trigonometric function values of an angle, given one trigonometric function of the angle Ch 8: Law of Cosines and Law of Sines, and Area of a triangle Use the laws of cosines and sines to solve a triangle Solve word problems using the laws of cosines and sines Find the Area of a triangle using A = 1/2bcsinA or Heron’s Formula Ch 9: Systems of Equations Solve a non-linear system by graphing or substitution Solve a linear system by graphing, substitution, or elimination(linear combination) Solve word problems involving linear systems Solve a 3x3 linear system algebraically and using the matrix feature on the calculator Find the maximum value of a linear programming problem by graphing the constraints and finding the corners. Ch 11: Sequences and Series Find the nth term in an arithmetic, geometric, or recursive sequence. Find a formula for the nth term in an arithmetic, geometric, or recursive sequence. Find the sum of a finite arithmetic series or a finite or infinite geometric series Use sigma notation to write a series Formulas to memorize: f ( x h) f ( x ) h Difference Quotient: Change to exponential form from logarithmic form and vice versus: log b x y b y x Vertex Form: y a( x h)2 k vertex is (h, k) Possible rational roots for a polynomial function: qxn + ….. + p roots are found by: ±factors of p divided by factors of q Quadratic Formula SOHCAHTOA Special Right Triangles, Quadrantal Angles Law of Sines: Law of Cosines: c 2 a 2 b 2 2ab cos C Area of a Triangle: the possible rational sin A sin B sin C a b c SAS: 1 bc sin A 2 SSS: s(s a)(s b(s c) , s log x MN log x M log x N M log x M log x N N log x M k k log x M Properties of Logarithms: log x r Compound Interest Formula: A P 1 n Continuous Compound Interest Formula: A Pe rt nt 1 a b c 2