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Review Topics: Midterm 2 will cover 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 7.1, & 7.2 Things to know… • Long Division (Polynomials) • Synthetic Division (Polynomials) • Complex Numbers o Standard Form o Powers of the imaginary unit i o Complex Conjugates o Add/Subtract o Multiply o Divide • Functions o Polynomials (Higher Degree) Find Complex Zeros Find all Zeros (Rational Zeros Test, Descartes’ Rule of Signs, Upper/Lower Bound rules, factoring, completing the square, quadratic formula) Write in Factored form Identify number of Zeros & and possible number of turns Identify the End Behavior Identify the domain Find x-intercept(s) & y-intercept o Rational Identify asymptotes (Vertical, Horizontal, Slant) – Note: Asymptotes are lines! Simplify Identify the domain Find x-intercept(s) & y-intercept Sketch o Exponential Evaluate Identify domain and range Identify horizontal asymptote Find x-intercept & y-intercept Sketch (using transformations) o Logarithmic Simplify Identify domain and range Identify vertical asymptote Find x-intercept & y-intercept Sketch (using transformations) • • • • • Understand the relationship between exponential and logarithmic functions Properties of logs and exponents o Use logarithmic properties to expand a log expression o Use logarithmic properties to condense a log expression o Use logarithmic properties to evaluate a log expression How to solve logarithmic and exponential equations Models (Exponential & Logarithmic) o Simple Interest (LINEAR) o Compound Interest o Continuously Compounded Interest o Exponential Growth or Decay o Logarithmic o Logistic Growth o Gaussian Systems of equations o Solve non-linear systems of equations By substitution By graphing o Solve linear 2x2 systems of equations By substitution By elimination By graphing Some Practice Problems… p. 209-211 #47-107 odd, 111-133 odd p. 212 #4-9, 11, 13, 14-16 p.271-274 #7-10, 11, 13, 23, 25, 35, 41-57 odd, 65, 67, 75-93 odd, 97113 odd, 119-129 odd, 135, 137-142, 145-147 p. 275 #15-25 odd p. 563 #5-11 odd, 19, 23, 25, 26, 27-30