What is a rational number? Which numbers have rational square roots? The decimal representation of irrationals. What is a real number?
What is a function? The domain and the range.
The graph of a function. Coördinate pairs of a function. The height of the curve at x.
15. Basic graphs
The constant function. The identity function.
Variables versus constants.
A polynomial equation. The roots of a polynomial.
Definition of the slope. Positive and negative slope. A straight line has only one slope.
The equation of the first degree. The graph of a first degree equation: a straight line.
Quadratic equation: Solution by factoring.
Solving a quadratic equation by completing the square. The quadratic formula.
The remainder theorem.
The factor theorem. The fundamental theorem of algebra. The integer root theorem. Conjugate pairs.
Concave upward, concave downward.
Reflection about the x-axis. Reflection about the y-axis. Reflection through the origin.
Symmetry with respect to the y-axis. Symmetry with respect to the origin. Test for symmetry.
Definition of a translation.
Singularities. The reciprocal function. Horizontal and vertical asymptotes.
Definition of inverses. Constructing the inverse.
The system of common logarithms.
The Fundamental Principle of Counting. Factorial representations.
A proof of the binomial theorem.
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