MAT 097 - Intermediate Algebra

3 Credits, 3 Contact Hours
3 lecture periods 0 lab periods

Definition of function and function notation, compound inequalities in one variable, graphs of linear inequalities in two variables, and absolute value equations and inequalities. Also includes rational and radical functions and equations, quadratic functions and their graphs, exponential functions and their graphs, and logarithms.

Prerequisite(s): Within the last three years: MAT 092  with a grade of C or better, or completion of module 25 in MAT 089A  or MAT 089B , or satisfactory score on the Mathematics assessment test.
Information: The online sections for the course require students to have the ability to share (electronically) handwritten work within the course.
  

1. Solve absolute value inequalities involving linear equations.
2. Solve rational equations with at least one factorable second-degree polynomial in the denominator.
3. Solve radical equations that result in a quadratic equation solvable by factoring.
4. Use the quadratic formula to solve quadratic equations that comes from an application problem.

1. Define and identify a function, and use function notation.
2. Solve compound inequalities in one variable and graph linear inequalities in two variables.
3. Solve absolute value equations and inequalities.
4. Simplify and perform operations on rational expressions, and solve rational equations.
5. Simplify radical expressions, convert between radical notation and rational exponents, and solve radical equations.
6. Solve quadratic equations by factoring, completing the square, and using the quadratic formula.
7. Graph quadratic functions.
8. Solve applications including literal equations.
9. Convert between exponential and logarithmic equations, and evaluate exponential and logarithmic expressions.
10. Graph elementary exponential functions.

        Optional Objectives

11. Factor polynomials using a variety of techniques.

12. Solve equations and applications involving variation.

1. Functions
   1. Definition
   2. Identification
   3. Notation
2. Inequalities
   1. Interval notation
   2. Compound
   3. Linear with two variables
   4. Applications
3. Absolute Value
   1. Equations
   2. Inequalities
4. Rational Expressions and Equations
   1. Domain of rational functions
   2. Addition, subtraction, multiplication, and division of rational expressions
   3. Complex rational expressions
   4. Rational equations including those that result in quadratic equations
   5. Applications including literal equations
5. Radical Expressions and Equations
   1. Domain of radical functions
   2. Addition, subtraction, multiplication, and division of radical expressions
   3. Rationalization of denominators or numerators
   4. Conversion between radical notation and rational exponents
   5. Radical equations
   6. Distance formula
   7. Applications including literal equations
6. Quadratic Equations and Functions
   1. Solve equations by factoring
   2. Complete the square
   3. Quadratic formula and interpretation of the discriminant
   4. Graph quadratic functions
   5. Applications including literal equations  
7. Exponential Functions and Logarithms
   1. Convert between exponential and logarithmic equations
   2. Evaluate exponential and logarithmic expressions
   3. Graph elementary exponential functions
8. Optional Topics
   1. Factoring polynomials
      1. Greatest common factor
      2. Factor by grouping
      3. Trinomials
      4. Difference of squares
      5. Difference/sum of cubes
   2. Variation

1. Direct
2. Inverse
3. Joint