Yes. You can start learning on Learnr for free. Learnr Pro unlocks higher daily limits and extra features.

Learn Precalculus

Build the function toolkit calculus will expect you to have.

Free to start. Built from a single prompt. No credit card.

Precalculus is the bridge between algebra and calculus, and its real subject is functions. You study how to read and transform graphs, compose and invert functions, and work with the main families: polynomial, rational, exponential, logarithmic and trigonometric. Many courses also cover sequences and series, conic sections, vectors, parametric and polar equations, and an informal first look at limits. Learnr builds a personalized precalculus course and teaches it through short interactive lessons, focusing on the algebra and graphing skills that most often trip people up later in calculus.

How to learn Precalculus, step by step

Patch any algebra gaps first. Factoring, rational expressions, exponent rules, radicals and solving quadratics appear in nearly every precalculus problem. Spend a week on them if needed, because algebra slips cause most errors at this level.
Think in functions and graphs. Practice finding domain and range, reading values from graphs and applying shifts, stretches and reflections such as f(x - 2) + 3 and -f(x). Use a graphing tool like Desmos to check your sketches.
Learn polynomial and rational functions. Find zeros by factoring and the rational root theorem, use multiplicity to sketch behavior at each zero, and locate vertical, horizontal and slant asymptotes of rational functions.
Master exponentials and logarithms. Learn that a logarithm is the inverse of an exponential, apply the product, quotient and power rules, and solve growth, decay and compound interest problems. The natural base e will matter a lot in calculus.
Cover trigonometry as functions. Connect the unit circle to the graphs of sine, cosine and tangent, learn the key identities and inverse functions, and solve trig equations. Short daily Learnr practice helps these values and identities stay automatic.
Finish with sequences, series and limits. Work with arithmetic and geometric sequences, sigma notation and the sum of an infinite geometric series, then explore limits numerically and graphically as a preview of calculus.

What you'll learn

Analyze functions by domain, range, intercepts and end behavior
Transform, compose and invert functions and their graphs
Work with polynomial and rational functions, including zeros and asymptotes
Solve exponential and logarithmic equations and model growth and decay
Use trigonometric functions, sequences and series with confidence

What's inside your Precalculus course

A sample path Learnr builds for Precalculus. Your real course adapts to your goal and level.

1. Functions, notation and graphs
2. Transformations, composition and inverses
3. Polynomial and rational functions
4. Exponential and logarithmic functions
5. Trigonometric functions and identities
6. Sequences, series and an introduction to limits

How long does it take to learn Precalculus?

A full precalculus course takes most learners about 3 to 6 months at 4 to 6 hours a week. If you only need a refresher before calculus, focusing on functions, logs and trig can take 4 to 8 weeks.

What you need before you start

Algebra 1 and 2 skills, including linear and quadratic equations, factoring and exponents, plus basic geometry. Prior trigonometry helps but is usually taught within the course.

Common mistakes to avoid

Treating f inverse of x as 1 over f(x). The inverse function undoes f, while 1/f(x) is the reciprocal.
Misusing log rules, for example writing log(a + b) as log a + log b. The product rule applies to log(ab), not to sums.
Moving a graph the wrong way, such as shifting f(x - 3) left instead of right. Test one point to check direction.

How Learnr builds your course

Type your topic

Tell Learnr you want to learn Precalculus, or get as specific as you like.

Get a personalized course

Learnr instantly builds a full Precalculus course tailored to your goal and skill level.

Learn and level up

Move through bite-sized lessons and interactive practice, earning XP and keeping your streak.

Precalculus questions, answered

Can I skip precalculus and go straight to calculus?

You can if your algebra, functions, logarithms and trigonometry are already solid. If any of those feel shaky, precalculus will save you time, because calculus courses assume them from the first week.

Is precalculus the same as trigonometry?

No, but trigonometry is usually a large part of it. Precalculus also covers polynomial, rational, exponential and logarithmic functions, plus topics like sequences and an introduction to limits.