# Intermediate Algebra: An Introduction to Functions through Applications, Preliminary Edition

Published Date: Aug 3, 1998

1. Introduction to Functions.

Graphical, numerical, and algebraic representations of functions.

Functional notation.

Evaluation of functions using the graphics calculator.

Applications of functions including interpretation of graphs.

Summary of mathematical and calculator concepts.

Problems.

2. Introduction to Linear Functions.

Construct tables using data from experiments and applications.

Determine whether data in a table represents a linear function.

Describe linear functions from verbal representations.

Determine the slope of a line given two points.

Graph linear functions from data (on graph paper and calculator).

Solve application problems involving direct variation.

Summary of mathematical and calculator concepts.

Problems.

3. Writing and Graphing Linear Equations and Inequalities.

Determine the equation of a line given one point and the slope or two points.

Use tables and the slope-intercept method to graph lines whose equation is given.

Solve linear equations in two unknowns for the dependent variable.

Solve and graph linear inequalities.

Solve application problems involving linear functions and inequalities.

Summary of mathematical and calculator concepts.

Problems.

4. Systems of Linear Functions.

Parallel and perpendicular lines.

Graphical and numerical solutions of linear systems.

Solution of systems of linear equations by substitution and elimination.

Graphical solutions of systems of linear inequalities.

Applications of systems of equations and inequalities.

Summary of mathematical and calculator concepts.

Problems.

5. Non-Linear Functions.

Determine if graph represents a function.

Identify the domain and range of a function.

Connect a graph with verbal representation.

Write inverse variation equations from an application.

Compare the graphs, domains, and ranges of power and exponential functions.

Summary of mathematical and calculator concepts.

Problems.

Identify and graph quadratic functions expressed in equation form.

Find vertices and intercepts of quadratic functions.

Describe effects of values of a and c on the graph of y = ax2 + bx + c.

Solve quadratic equations algebraically, graphically, and numerically.

Write quadratic equations from applications.

Use Pythagorean Theorem as appropriate.

Solve and interpret quadratic inequalities graphically.

Summary of mathematical and calculator concepts.

Problems.

7. Radical, Rational, and Piecewise-Defined Functions.

Graph and find the domain and range or rational functions.

Graph and find the domain and range or radical functions.

Graph and find the domain and range or piecewise defined functions.

Solve equations with radicals.

Applications of radical, rational, and piecewise functions.

Summary of mathematical and calculator concepts.

Problems.

8. Exponential, Logarithmic, and Logistic Functions.

Determine the inverse of a function if it exists.

Explore log(x) as the inverse of exx.

Explore log(x) as the inverse of 10x.

Graph and find the domain and range of logarithmic functions.

Graph and find the domain and range of exponential functions.

Graph and find the domain and range of logistic functions.

Approximate a logistic function with a piecewise defined function.

Applications of logarithmic, exponential, and logistic functions.

Summary of mathematical and calculator concepts.

Problems.

Appendix A: Pretest of Prerequisite Skills.

Pretest keyed to review exercises.

Exercises covering the prerequisite Elementary Algebra skills needed for Intermediate Algebra.

B: Using the TI-83 Graphing Calculator.

Directions for using the TI-83 in Intermediate Algebra.

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