Math 110 Exam 1 Questions and Answers Updated/Verified

Finding Domain - ANSWER-Rule 1) Cannot divide by zero set denominator to zero and solve Finding Domain - ANSWER-Rule 2) cannot take the square root of negative number set what is inside radical >= 0 and solve *make number lines* Polynomial Function - ANSWER-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 - ANSWER-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 - ANSWER-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... - ANSWER-but the reverse is not true! Not all power functions are polynomial functions Equilibrium Point - ANSWER-occurs where the supply function equals the demand function s(x) = d(x) To find equilibrium *quantity* - ANSWER-set s(x)=d(x) and solve for x To find equilibrium *price*, p - ANSWER-set s(x)=d(x) and solve for x and plug it back into either s(x) or d(x) Demand p(x) - ANSWER-p denotes price and x is the amount produced Revenue R(x) - ANSWER-R(x)= x * p(x) Total Cost C(x) - ANSWER-Fixed cost + variable cost Avg. Cost - ANSWER-C(x) / x Profit P(x) - ANSWER-R(x) - C(x) Break Even Level - ANSWER-Where R(x) = C(x) or Where P(x) = 0 Limits - ANSWER-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 - ANSWER-This tells you to SIMPLIFY by either: - factoring - multiplying by the conjugate - finding a common denominator CASE 2: limits with a #/0 - ANSWER-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... - ANSWER-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... - ANSWER-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 - ANSWER-When you are taking limits as x approaches +- infinity, you want to look at the highest power on top and bottom