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College Algebra

College Algebra. Review for final exam. Chapter 2 – Functions and Graphs. Increasing/decreasing parts of functions Combining functions with +,-,x,/ Composing/decomposing functions Creating functions/formulas from information in word problems Finding domains of functions.

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College Algebra

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  1. College Algebra Review for final exam

  2. Chapter 2 – Functions and Graphs • Increasing/decreasing parts of functions • Combining functions with +,-,x,/ • Composing/decomposing functions • Creating functions/formulas from information in word problems • Finding domains of functions

  3. Chapter 3 – Quadratic Functions • Find zeros using factoring or quadratic formula • Vertex is at This gives the maximum or minimum of the function • , so . Other than that, works just like any other variable

  4. Ch. 3 continued • Word problems about max/min • Solving “quadratics in disguise” • Solving rational equations (multiply through by common denominator; make sure to check answers)

  5. Ch. 4 – Polynomial and Rational Fns • Characteristics of graphs of polynomials – end behavior, y-intercept, x-intercepts • Dividing polynomials (synthetic or long) • Possible rational zeros • Check possibilities using synthetic division to find actual zeros, factorization

  6. Chapter 4 continued • Characteristics of rational functions – domain, x-intercepts, y-intercept • Solving polynomial and rational inequalities using the test value method (solutions in interval notation)

  7. Ch. 5 – Inverse Fns, Exponents, and Logs • How to tell if a fn is 1-to-1 (has an inverse) • How to find the inverse of a fn • Domain, properties of exponential functions • Compound interest • Domain, properties of log functions • Converting exponential/log form • Find value of logs

  8. Ch. 5 continued • Solve exponential and log equations (by converting to other form, using properties, etc.) • Exponential growth/decay • Doubling time/half-life

  9. Ch. 6 – systems of equations • Solve using substitution, elimination, or matrices – your choice • Word problems that give systems of equations

  10. Ch. 7 – Conic sections • Recognizing conics from equations • General shape of graphs • Finding vertex, focus, directrix of parabola • Finding center of circle, ellipse, hyperbola • Solving systems of equations involving conic sections – use substitution if one eq is linear

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