Math 110 Exam New 2024 Version Best Studying Material with All Questions from Actu al Exam and 100% Correct Answers Finding Domain - Correct Ans - Rule 1) Cannot divide by zero set denominator to zero and solve Finding Domain - Correct Ans - Rule 2) cannot take the square root of negative number set what is inside radical >= 0 and solve *make number lines* Polynomial Function - Correct Ans - ex: f(x)= 2x^4 + 3x^2 - 10x all powers must be *non negative whole numbers* cannot have negative powers, square roots, or fractional powers the *degree* of the function is the highest power (in this case 4) Rational Function - Correct Ans - ex: f(x)= (x^3 +5x^2 -7) / x+1 It is the QUOTIENT of 2 polynomials This means NO negative powers, square roots or fractional powers *does NOT have a degree* Power Function - Correct Ans - ex: f(x)= 2x^5, 3x^ -2, square roots, etc Powers can be any real number (including negatives and fractions) *does NOT have a degree* All polynomial functions are power functions... - Correct Ans - but the reverse is not true! Not all power functions are polynomial functions Equilibrium Point - Correct Ans - occurs where the supply function equals the demand function s(x) = d(x) To find equilibrium *quantity* - Correct Ans - set s(x)=d(x) and solve for x To find equilibrium *price*, p - Correct Ans - set s(x)=d(x) and solve for x and plug it back into either s(x) or d(x) Demand p(x) - Correct Ans - p denotes price and x is the amount produced Revenue R(x) - Correct Ans - R(x)= x * p(x) Total Cost C(x) - Correct Ans - Fixed cost + variable cost Avg. Cost - Correct Ans - C(x) / x Profit P(x) - Correct Ans - R(x) - C(x) Break Even Level - Correct Ans - Where R(x) = C(x) or Where P(x) = 0 Limits - Correct Ans - The limit is the *y -value* that a function *approaches* as it gets closer and closer to a given x -value You start every limit by plugging in the x value CASE 1: limits with a 0/0 - Correct Ans - This tells you to SIMPLIFY by either: - factoring - multiplying by the conjugate - finding a common denominator CASE 2: limits with a #/0 - Correct Ans - If you plug in and get a #/0 : - The limit *does not exist* - The answer will be infinity, negative infinity or DNE - visually this is a vertical asymptote These are typically one sided limits... - Correct Ans - To solve, plug in a number, on the correct side of the limit, close to the x value that the limit is approaching. Determine whether the answer will be negative or positive If it is not a one sided limit... - Correct Ans - you must compute the limit coming from both sides if you get the same thing then that is the answer if you get two different answers, then the limit is DNE Limits as x approaches + - infinity - Correct Ans - When you are taking limits as x approaches + - infinity, you want to look at the highest power on top and bottom
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