Larson/Hostetler/Edwards Precalculus with Limits, High School Edition, 5e — a Cengage / National Geographic Learning HS-binding of the dominant college PrecalcLimits text by Ron Larson, Robert P. Hostetler, and Bruce H. Edwards. HS Edition preserves identical major-topic scope and Ch P + Ch 1-11 structure as the college Larson Precalculus with Limits 5e : prerequisites, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, trigonometry, analytic trigonometry, additional topics in trigonometry, systems of equations and inequalities, matrices and determinants, sequences/series/probability, topics in analytic geometry, and a dedicated Ch 11 'Limits and an Introduction to Calculus' that previews calc 1 (limits, tangent line problem, area problem). 12 chapters (Ch P + Ch 1-11).
Foundational algebra review: real numbers, exponents, radicals, polynomials, factoring, and rational expressions, refreshing the prerequisite skills students need before precalculus topics begin.
The Cartesian coordinate system, graphs of equations, lines, functions and their analysis (domain, range, increasing/decreasing, even/odd), library of parent functions, transformations, function operations and composition, inverse functions, and mathematical modeling/variation.
Quadratic functions and models, polynomial functions of higher degree (end behavior, zeros), polynomial division (long, synthetic), complex numbers, the fundamental theorem of algebra, rational functions and their graphs, and nonlinear inequalities.
Exponential functions and their graphs (including the natural exponential), logarithmic functions and their graphs (common and natural log), properties of logarithms, exponential and logarithmic equations, and applications/models including growth, decay, and compound interest.
Radian and degree measure, the unit circle and trigonometric functions, right triangle trigonometry, trigonometric functions of any angle, graphs of the six trigonometric functions, inverse trigonometric functions, and applications/models.
Fundamental trigonometric identities, verifying identities, solving trigonometric equations, sum and difference formulas, multiple-angle and product-to-sum formulas.
Law of Sines (including the ambiguous case), Law of Cosines, vectors in the plane, dot product and angle between vectors, complex plane, and trigonometric/polar form of complex numbers including powers and roots.
Linear and nonlinear systems of equations, two-variable and multivariable linear systems.
Matrices as systems-of-equations representation, matrix operations (add, multiply, scalar multiply), inverse of a square matrix, determinants and Cramer rule.
Sequences and series, arithmetic sequences and partial sums, geometric sequences and series, and the binomial theorem.
Lines, conic sections (parabolas, ellipses, hyperbolas), polar coordinates and graphs of polar equations.
A precalc-level preview of calculus: introduction to limits, techniques for evaluating limits, the tangent line problem (precursor to derivatives), limits at infinity and limits of sequences, and the area problem (precursor to integrals). Cross-listed from M2231 (Calculus 1) since DCM M1431 does not include limits/derivatives - same approach used at C9 for Sullivan Ch 14 + Stewart Ch 12.