MTH 124 Exam 1 Study Guide Interval Notation (What does a bracket mean, what does parentheses mean? What does U stand for?) • Bracket: Includes point • Parentheses: does not include point • U: union Function • Functions tell us dependence of quantity on another Types of Functions to know • Linear • Quadratic • ExponentialIf you want to learn more check out bu cs 111
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• Rational • Polynomial Linear Function • y = mx + b Quadratic Function • f(x) = ax^2 + bx + c Exponential Function• f(x) = Ab^x Rational Function • f(x) = p(x) / q(x) Polynomial Function • f(x) = a_n x^n +a_n-1 x^n-1 + ... +a_ Slope • m = slope = change in y/change in x • (y2 - y1) / (x2 - x1) What does b stand for in a linear function? • the y-intercept What does cost equal? • Cost = variable cost + fixed cost • c(x) = mx + b Revenue • Total income Profit • Profit = revenue - costHow do you break even? • Profit has to = 0, so revenue has to = cost Quadratic Formula • x = [-b +/- sqrt(b^2 - 4ac)] / (2a) What do you have to do with all of your answers? • LABEL • Show work • Explain answer Exponential growth • If b > 1 (slope will be going in I and II if A > 0) (slope will be in III and IV if A < 0) • Remember Exponential Function: f(x) = Ab^x • A is where the slope intercepts with the y-axis (a constant) Exponential decay • If b < 1 (slope will be going in I and II if A > 0) (slope will be in III and IV if A < 0) • Remember Exponential Function: f(x) = Ab^x • A is where the slope intercepts with the y-axis (a constant) Compound and Continuous Interest Equation • A(t) = P[1+(r/m)]^mt• P = principal (money started with) • r = interest rate (in decimal) • m = # of times compunded per year • t = time Compounded Continuously Equation • A(t) = Pe^rt • P = principal (money started with) • e = (a constant - on your calculator) • r = interest rate (in decimal) • t = time Logarithmic Functions log_b x "log base b of x" or "log of x base b" is the power we need to raise b to get to x. Log Properties • log_b (xy) = log_b x + log_b y • log_b (x/y) = log_b x - log_b y • log_b (x^r) = r*log_b (x) • log_b (x) = log_a (x)/log_a (b) = change of base formula • log_b (b) = 1 • log_b (1) = 0 • log_b (1/x) = log_b (1) - log_b (x) = -log_b(x) • log_b (b^x) = x log_b (b) = x • b^log_b x = xAverage Rate of Change • AROC = f(b) - f(a) / b - a Slope of Secant • f(x+h) - f(x) / h Limits • lim_h->0 f(x+h) - f(x) / h Logistic Equation (population growth) • y(t) = L / (1 + Ae^-kt) • y = population • L = carrying capacity • A & k = constant related to growth • t = time • e = constant on your calculator How will Exam 1 be laid out? • True/False • Multiple Choice • Short Answer