Math 116 - Chapter 1 & 2 Study Guide

  1. Find the equation of the line that passes through the given points.
  2. State the domain of the function. Three parts.
  3. Given a function h, decompose it into two functions f and g. Two parts.
  4. Find an equation having the given solutions. Leave your answer in factored form.
  5. Given a function, evaluate it at the specified values and simplify. Three parts.
  6. Determine if the equation represents y as a function of x. Four parts.
  7. Solve the formula for the indicated variable.
  8. Given a table of values for x, f(x), and g(x), find the combination, composition, and inverse of functions. See example at bottom of this page. Eight parts.
  9. Consider the graph of the function y=f(x) with the given domain and range. In each case identify the translation in English and give the domain and range of the translated function. Five parts. Look at your notes or the section 1.5 online lecture notes.
  10. Solve the quadratic equation by factoring.
  11. Solve the quadratic equation by extraction of roots.
  12. Solve the quadratic equation by completing the square.
  13. Solve the quadratic equation by using the quadratic formula.
  14. Perform the indicated operations with complex numbers and simplify. Write your answers in standard form. Four parts.
  15. Know the equations and graphs of the basic functions. Constant, Linear (identity), Quadratic (squaring), Cubic, Square Root, Absolute Value, and the Greatest Integer Function. Identify the common function and the transformation of the graph; also write the formula for the graphed function. Also look at your take home exam, but that only required you to find the equation. This problem also wants you to name the basic function and describe the translation.
  16. Find all solutions of the equation. Use any algebraic method, but show work. Three parts.
  17. Solve the inequality and sketch on the real number line. Write your answers in interval notation. Two parts.


Example for #8

x 1 2 3
f(x) -1 5 1
g(x) 3 1 -1

Points per problem

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total
Pts 2 3 2 2 3 4 2 8 10 3 3 3 3 4 10 9 4 75