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concepts for math - Concept Review Math 107 Final Exam 1...

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Concept Review: Math 107 Final Exam 1. Solving equations: Factor: (by grouping or by rational zeros theorem for polynomials) Understand and utilize algebraic operations (e.g. combining fractions, laws of exponents, laws of logarithms, reducing exponentials, getting rid of logs, properties of inverse functions, completing the square, ...) Plug variables into a function (average rate of change, exponential models,...) Check solutions against the domain restrictions 2. Solving inequalities: Use when determining domain restrictions Know when the direction changes (e.g. absolute value inequalities: think bounded or unbounded) 3. Domains: Use interval notation except for with infinite breaks (e.g. tan( x ) , cot( x ) , ... ) Start from original equation (not simplified version) List how you restrict the domains of these three types of problems: *Even roots (e.g. f ( x ) = f ( x ) 0) *Dividing by zero: (e.g. 1 f ( x ) = f ( x ) = 0) *Logarithms: (e.g. log a f ( x ) = f ( x ) > 0) For inverse trig functions, think about the range of the original function
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