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COURSE DESCRIPTION:
A. Introduction to Functions, Models and Graphs.
B. Linear Functions and their applications.
C. Quadratic Functions and their applications.
D. Root Functions, Rational Exponents, Radicals.
E. Exponential Functions, an introduction.
COURSE OBJECTIVES:
To engage students in graphical and numerical mathematical thinking.
To study algebraic techniques and when to use these techniques;
to encourage students to think, not just repeat examples in the text.
To teach students to use mathematics to think critically.
To incorporate applications of mathematics which engage students and demonstrate the usefulness of mathematics.
COURSE CONTENT:
The course will include but is not restricted to a discussion of the following topics.
Exponents: integer and rational; scientific notation.
Polynomial arithmetic: addition, subtraction, and multiplication of single variable polynomials.
Linear Functions: graphs; equations; slope, slope-intercept form of equations, writing equations for lines;
inequalities - solving graphically and algebraically;Linear Systems of equations (2x2) and their applications.
Quadratic Functions: factoring; solving quadratic equations; the quadratic formula; graphing; vertex: maximum,
minimum values of quadratic functions; applications of quadratic functions.
Optional: non-linear systems and completing the square.
Complex Numbers: definition of i, i2; connection between complex roots of an equation
and the graph of a quadraticfunction.
Radicals and Rational Exponents: rules for radicals; simplifying radical expressions; operations with rational
exponents - confined to one variable case.
Exponential Functions of form f(x) = abx.
Graphing: the effect of the values of a, b, and x on the graph of the function. Logs
and the use of the log key on the calculator to solve exponential equations.
Applications will be emphasized along with the algebra skills
necessary to treat the included applications.
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