What Is Intermediate Algebra?

• review the concept of number, study the fundamentals of logic and set theory, review solving equations and inequalities, then apply what they've learned to the study of compound inequalities;
• study the definition of a function, determine the domain and range of a function, work with function notation, learn how to draw and interpret the graph of a function (both manually and with a graphing calculator), learn how to solve equations and inequalities by graphing, and learn how to apply specific transformations (scaling, reflecting, and translating) to the graph of a function;
• study linear models, determine the relation between rate and the slope of a line, study both the slope-intercept and point-slope forms of a line, then apply this knowledge to various applications, including linear regression;
• study piecewise functions and their graphs and their application to absolute value functions, then use the graphs to determine the solution(s) of equations and inequalities containing the absolute value;
• study the basic graph of y = x², then apply various transformations until the vertex form of a parabola, y = a(x-h)²+k, is well understood, use the technique of completing the square to identify the vertex and axis of symmetry, use both factoring and the quadratic formula to identify the zeros of the quadratic function, then study applications of the quadratic function, including motion and optimization;
• study the polynomial function, determining the relationship between the degree, leading coefficient, and end-behavior, identifying the zeros by factoring, drawing the graph of the polynomial and identifying extrema, then applying that knowledge to applications involving optimization;
• study the basic graph of y = 1/x and apply the usual transformations, reduce rational expressions to lowest terms, identify zeros and asymptotes of rational functions and use this information to draw the graph (both manually and with graphing calculator), add, subtract, multiply, and divide rational expression and identify restrictions, solve rational equations, and work with various applications that involve the use of rational expressions (work, rate, etc.);
• define the exponential function for all real valued exponents (natural number, whole number, integers, rational numbers, and real exponents), study the graph of the exponential function (growth and decay) and understands its asymptotic behavior, study discrete and continuous compounding of interest, introduce the number "e," study the definition of the inverse of a function and apply the inverse concept to define the logarithmic function, determine properties of the logarithm (particularly the change of base property), and apply the logarithm and exponential to various applications of growth and decay.
• study the square root function and apply various transformations to the basic graph, place radical expressions in "simple form," solve equations containing radical expressions, and study the Pythagorean theorem and its various applications (distance formula, etc.);

What Are The Prerequisites?

Syllabus

Homework

Examinations

Sample Activities

Online Testing

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