College Algebra Resources

Review Problems

Objectives 1-5 | Objectives 6-10 | Objectives 11-15 | Objectives 16-17

List of Objectives

• Objective 1
  • Objective 1a - Get complete graphs of functions.
  • Objective 1b - Find domains and ranges of functions.
  • Objective 1c - Evaluate functions.
  • Objective 1d - Translate applied problems to function notation for graphing and solving.
  • Objective 1e - Find intervals where a function is increasing and decreasing.
  • Objective 1f - Find the zeros and local extrema of functions.
• Objective 2 - Understand graph shifts, reflections, and stretches for general functions.
• Objective 3 - Write and evaluate compositions of functions.
• Objective 4
  • Objective 4a - Determine if a function has an inverse.
  • Objective 4b - Find the inverse of a function.
• Objective 5 - Use functions to solve applied problems.

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• Objective 6
  • Objective 6a - Solve polynomial and rational inequalities both algebraically and using the grapher.
  • Objective 6b - Use inequalities to solve applied problems.
• Objective 7 - Find the real and complex zeros of a polynomial function and interpret polynomial zeros and graphs.
• Objective 8
  • Objective 8a - Find the vertical and horizontal or slant asymptotes of the graph of a rational function.
  • Objective 8b - Graph rational functions.
• Objective 9 - Graph exponential and logarithmic functions and interpret their graphs.
• Objective 10
  • Objective 10a - Use the properties of logarithms to expand and condense logarithms.
  • Objective 10b - Use the properties of logarithms to solve logarithmic equations.

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• Objective 11
  • Objective 11a - Solve exponential equations algebraically and/or using the graphing calculator.
  • Objective 11b - Solve applied problems using logistic, exponential growth, and exponential decay models.
• Objective 12
  • Objective 12a - For a given data set, find the linear regression equation and use it for prediction.
  • Objective 12b - Recognize and interpret an appropriate linear correlation coefficient.
• Objective 13
  • Objective 13a - Using row operations, write an augmented matrix in reduced row-echelon form.
  • Objective 13b - Write solutions from reduced matrices including infinite-solution and no-solution matrices.
• Objective 14
  • Objective 14a - Use the inverse of a matrix for solving systems of linear equations.
  • Objective 14b - Solve problems involving systems of linear equations.
• Objective 15
  • Objective 15a - Write a sequence given the n^th term and find the n^th term of a given sequence.
  • Objective 15b - Use and simplify summation and factorial notation and find partial sums of series.

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• Objective 16
  • Objective 16a - Identify arithmetic sequences and series and find the common difference, the n^th term, and the n^th partial sum.
  • Objective 16b - Use arithmetic sequences and series to solve problems.
• Objective 17
  • Objective 17a - Identify geometric sequences and series and find the common ratio, the n^th term, and the n^th partial sum.
  • Objective 17b - Find the sum of an infinite geometric series and use geometric sequences and series to solve problems.