Precalculus Calculators

Precalculus is where algebra turns into the study of functions. You learn how functions are built, combined and undone, and how logarithms and rational expressions behave, all of which calculus takes for granted. These calculators perform each operation exactly and explain the reasoning behind every step.

Calculators

Logarithm Calculator

Evaluate $\log_b(x)$ in any base, including $e$ and 10, or solve $b^x = y$ and $\log_b(x) = c$ , with exact answers whenever the numbers allow.

Polynomial Calculator

Expand, add, subtract, multiply or divide polynomials, evaluate one at a point, or find its real roots, with exact arithmetic and every step written out.

Rational Expression Calculator

Simplify an algebraic fraction, or add, subtract, multiply and divide two of them, with factoring, common denominators and excluded values shown at every step.

Inverse Function Calculator

Enter a function f(x) to find its inverse f⁻¹(x) by swapping x and y and solving, with the inverse's domain and an automatic check that the two functions undo each other.

Function Composition Calculator

Enter f(x) and g(x) to build f∘g, g∘f, f∘f or g∘g, simplify it, evaluate it at any point and see the domain of the composite function.

Domain and Range Calculator

Enter a function f(x) to get its domain and range in interval notation, with every restriction from denominators, square roots and logarithms worked out step by step.

Topics covered

Logarithms: Logs in any base, plus exponential and logarithmic equations solved exactly.
Polynomials and rational expressions: Expanding, dividing and finding roots of polynomials, and simplifying rational expressions.
Functions: Inverse functions, composition, and the domain and range of a formula.

What you will practise here

Precalculus problems usually ask you to rewrite something into a more useful form. A logarithm is rewritten with the change of base rule, a polynomial is divided to reveal its factors, a rational expression is simplified while keeping track of the values that make the denominator zero, and a function is reversed to find its inverse. The calculators perform each rewrite exactly and keep the restrictions that the rewrite would otherwise hide.

Questions about functions are often about where they make sense. The domain and range calculator solves the inequalities that keep square roots and logarithms defined and denominators nonzero, and the composition calculator applies those rules to $f(g(x))$ , where the inner function can remove values from the domain.

How this prepares you for calculus

Limits, derivatives and integrals all assume fluent algebra with functions. Simplifying a rational expression is exactly what you do to evaluate many limits, inverse functions explain why $\ln x$ and $e^x$ undo each other, and polynomial division is the first step in integrating rational functions. Working through these calculators step by step builds the habits that make calculus problems shorter and more reliable.

Courses and topics

Topic explainers with worked examples, common mistakes and practice questions in Precalculus.

Precalculus

High school · 3 topic explainers

The function toolkit needed for calculus.

Guides

How to Solve Quadratic Equations: Factoring, Completing the Square and the Formula
Factoring is fastest when it works, completing the square explains where the formula comes from, and the quadratic formula always works. Here is how to choose, with every example checked.
How to Check Your Math Homework and Answers
Almost every math answer can be checked without the answer key. Substituting back, working in reverse, estimating, testing special values and checking units catch the large majority of errors in a fraction of the time the original work took.