Precalculus Exercises

Hailey's exercise sets from Precalculus with Limits: A Graphing Approach (Larson).

Each set: one question at a time, with a 💡 step-by-step solution button for every question.

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Exercise sets

1.1

Lines in the Plane

129 questions · 29 exercise groups · 665 worked solution steps · 6 figures taken from the PDF · 11 questions point to a textbook figure

Vocabulary and concept checks, slope from two points, point-slope and slope-intercept forms, parallel and perpendicular lines, real-world linear modelling, and the cumulative mixed review.

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Source PDF: ~/Downloads/precalc_1.1.pdf · added 2026-09-14

1.2

Functions

98 questions · 11 exercise groups · 460 worked solution steps · 17 figures taken from the PDF · 0 questions point to a textbook figure

Testing relations for functionhood, evaluating functions, finding domains and ranges, difference quotients, and piecewise-defined functions.

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Source PDF: ~/Downloads/precalc_1.2.pdf · added 2026-09-14

1.3

Graphs of Functions

122 questions · 14 exercise groups · 630 worked solution steps · 26 figures taken from the PDF · 1 questions point to a textbook figure

Reading function values from graphs, domain and range, the vertical line test, zeros, increasing and decreasing intervals, relative extrema, and the greatest integer function.

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Source PDF: ~/Downloads/precalc_1.3.pdf · added 2026-09-14

1.4

Shifting, Reflecting, and Stretching Graphs

84 questions · 9 exercise groups · 432 worked solution steps · 14 figures taken from the PDF · 0 questions point to a textbook figure

Vertical and horizontal shifts, reflections in the axes, nonrigid stretches and shrinks, and writing equations of transformed graphs.

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Source PDF: ~/Downloads/precalc_1.4.pdf · added 2026-09-14

1.5

Combinations of Functions: Composite Functions

102 questions · 13 exercise groups · 553 worked solution steps · 4 figures taken from the PDF · 6 questions point to a textbook figure

Sum, difference, product and quotient functions with their domains, composite functions, and decomposing a function into a composition.

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Source PDF: ~/Downloads/precalc_1.5.pdf · added 2026-09-14

1.6

Inverse Functions

144 questions · 19 exercise groups · 755 worked solution steps · 3 figures taken from the PDF · 19 questions point to a textbook figure

The inverse of a function, verifying that two functions are inverses, finding inverses algebraically, one-to-one functions, and graphs of inverse functions.

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Source PDF: ~/Downloads/precalc_1.6.pdf · added 2026-09-14

1.7

Linear Models and Scatter Plots

34 questions · 5 exercise groups · 193 worked solution steps · 8 figures taken from the PDF · 0 questions point to a textbook figure

Scatter plots, correlation, fitting a line to data by eye, least-squares regression lines, and using linear models to predict.

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Source PDF: ~/Downloads/precalc_1.7.pdf · added 2026-09-14

ch1-review

Chapter 1 Review

110 questions · 28 exercise groups · 592 worked solution steps · 14 figures taken from the PDF · 0 questions point to a textbook figure

Every exercise from the Chapter 1 Review (Functions and Their Graphs), grouped by section so a section can be revised on its own — with each section's printed "What Did You Learn?" recap, one question at a time and a step-by-step solution for every one.

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Source PDF: ~/Downloads/precalc_1_review.pdf · added 2026-09-15

ch2-review

Chapter 2 Review

166 questions · 34 exercise groups · 894 worked solution steps · 0 figures taken from the PDF · 6 questions point to a textbook figure

Every exercise from the Chapter 2 Review (Polynomial and Rational Functions), grouped by section so a section can be revised on its own — with each section's printed "What Did You Learn?" recap, one question at a time and a step-by-step solution for every one.

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Source PDF: ~/Downloads/precalc_2.review.pdf · added 2026-09-15

2.1

Quadratic Functions

89 questions · 16 exercise groups · 487 worked solution steps · 0 figures taken from the PDF · 18 questions point to a textbook figure

Graphing quadratic functions in standard form, the vertex and axis of symmetry, identifying x-intercepts, writing the equation of a parabola from its graph, and optimization word problems.

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Source PDF: ~/Downloads/precalc_2.1.pdf · added 2026-09-15

2.2

Polynomial Functions of Higher Degree

128 questions · 19 exercise groups · 664 worked solution steps · 9 figures taken from the PDF · 7 questions point to a textbook figure

End behaviour and the Leading Coefficient Test, real zeros and their multiplicities, the Intermediate Value Theorem, and sketching polynomial graphs.

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Source PDF: ~/Downloads/precalc_2.2.pdf · added 2026-09-15

2.3

Real Zeros of Polynomial Functions

120 questions · 21 exercise groups · 668 worked solution steps · 0 figures taken from the PDF · 10 questions point to a textbook figure

Long division and synthetic division, the Remainder and Factor Theorems, the Rational Zero Test, Descartes's Rule of Signs, and locating real zeros.

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Source PDF: ~/Downloads/precalc_2.3.pdf · added 2026-09-15

2.4

Complex Numbers

98 questions · 13 exercise groups · 489 worked solution steps · 2 figures taken from the PDF · 0 questions point to a textbook figure

The imaginary unit i, standard form a+bi, addition/subtraction/multiplication of complex numbers, complex conjugates, quotients in standard form, and complex solutions of quadratic equations.

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Source PDF: ~/Downloads/precalc_2.4.pdf · added 2026-09-15

2.5

The Fundamental Theorem of Algebra

78 questions · 13 exercise groups · 433 worked solution steps · 6 figures taken from the PDF · 0 questions point to a textbook figure

The Fundamental Theorem of Algebra, complex zeros and conjugate pairs, factoring a polynomial completely, and building a polynomial from its zeros.

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Source PDF: ~/Downloads/precalc_2.5.pdf · added 2026-09-15

2.6

Rational Functions and Asymptotes

66 questions · 12 exercise groups · 359 worked solution steps · 0 figures taken from the PDF · 15 questions point to a textbook figure

The domain of a rational function, vertical and horizontal asymptotes, holes, and limits at infinity.

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Source PDF: ~/Downloads/precalc_2.6.pdf · added 2026-09-15

2.7

Graphs of Rational Functions

101 questions · 16 exercise groups · 573 worked solution steps · 0 figures taken from the PDF · 9 questions point to a textbook figure

Sketching rational functions by hand: intercepts, vertical and horizontal asymptotes, slant asymptotes, holes, and behaviour near the asymptotes.

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Source PDF: ~/Downloads/precalc_2.7.pdf · added 2026-09-15

2.8

Quadratic Models

40 questions · 7 exercise groups · 220 worked solution steps · 0 figures taken from the PDF · 9 questions point to a textbook figure

Scatter plots and correlation, fitting linear and quadratic models to data, coefficients of determination, and using a model to predict.

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Source PDF: ~/Downloads/precalc_2.8.pdf · added 2026-09-15