从第一原理掌握 Pre-Calculus
Functions, trigonometry, sequences, conic sections, and analytic geometry — the bridge between Algebra 2 and Calculus. Covers TEKS §111.42.
Functions: Domain, Range, and Notation You Actually Need
Master the language of functions — what domain and range really mean, how to read function notation, and why piecewise functions trip students up.
Function Transformations: Shift, Stretch, Reflect
The four basic transformations of a function — how to spot them from an equation and predict the new graph in seconds.
Polynomial Functions: Zeros, Multiplicity, and End Behavior
Why some zeros "bounce" off the x-axis while others cross — and how the leading term decides what happens far from zero.
Rational Functions: Asymptotes, Holes, and What to Do at Each
Vertical asymptote vs. hole — the cancellation rule that decides which. Plus horizontal and slant asymptote shortcuts.
Exponential and Logarithmic Functions: Inverses That Run Your World
Why exp and log are inverses, the three log rules that solve everything, and the domain trap that sinks log equations.
The Unit Circle: Special Angles You Must Memorize
The unit circle is the source of all trigonometry. Master these five special angles and signs by quadrant — everything else builds from here.
Trig Identities and Equations: The Six That Solve Everything
Pythagorean, double-angle, and half-angle identities — when to apply each and how to find all solutions in [0, 2π].
Sequences and Series: Arithmetic, Geometric, and Sigma
The four formulas that handle every Pre-Calc sequence question — plus the convergence rule that decides whether an infinite sum exists.
Conic Sections: Circle, Ellipse, Parabola, Hyperbola
The four conics and how their standard forms reveal vertices, foci, and asymptotes at a glance.
Vectors and Polar Coordinates: Two Ways to Locate a Point
Vector operations, dot products, and how polar coordinates convert to rectangular — the building blocks of physics and engineering math.