1.1Real Numbers and InequalitiesNumber sets, interval notation, and solving inequalities, including absolute value.Number lines for the intervals (−1, 4], [2, ∞) and (−3, 3). Open circles mark endpoints that are not included, closed circles mark endpoints that are included.(−1, 4]−1 < x ≤ 4−5−4−3−2−1012345[2, ∞)x ≥ 2−5−4−3−2−1012345Not startedPractice
1.2FunctionsDomains, equal functions, operations on functions, and composition.Graph of y = √x. Square root starting at the origin. Domain: x ≥ 0.y = √xGraph of y = 1/x. Two branches, not defined at x = 0. Domain: x ≠ 0.y = 1/xNot startedPractice
1.3Inverse FunctionsOne-to-one functions, the horizontal line test, and finding inverses with their domain and range.Graph of f(x) = x² for x ≥ 0 and its inverse f⁻¹(x) = √x, mirrored across the dashed line y = x. The point (2, 4) on f matches the point (4, 2) on the inverse.f(x) = x²f⁻¹(x) = √xy = xNot startedPractice
1.4Trigonometric Functions and their InversesRadians, exact values, quadrant signs, identities, and inverse trig ranges.Unit circle with the points for 0, π/6, π/4, π/3, π/2, π and 3π/2: (1, 0), (√3/2, 1/2), (√2/2, √2/2), (1/2, √3/2), (0, 1), (−1, 0) and (0, −1). Quadrant signs: Q I all positive, Q II sin, Q III tan, Q IV cos.ASTC0π/6π/4π/3π/2π3π/2Not startedPractice
2.1Definition of LimitReading limits from graphs and tables, and comparing left and right limits.A graph that jumps at x = a. From the left it approaches L₁ and from the right it approaches L₂. The one-sided limits are different, so the limit at a does not exist.aL₁L₂L₁ ≠ L₂: limit does not existNot startedPractice
2.2Limit LawsLimit laws, the 0/0 form, factoring, conjugates, and the squeeze theorem.A curve with a hole at x = a. From the left and from the right the curve approaches the same height L, so the limit as x approaches a equals L.aLlimit = LNot startedPractice
2.3Limits Involving Infinity and Asymptotic BehaviorInfinite limits, limits at infinity, and vertical and horizontal asymptotes.Graph of y = 1/(x − 1) + 2 with a dashed vertical asymptote x = 1 and a dashed horizontal asymptote y = 2.x = 1y = 2y = 1/(x − 1) + 2Not startedPractice