Elementary Algebra and Functions

Explore numbers and expressions; equations and inequalities; functions and growth. Concepts and connections are available independently of video coverage.

Prerequisites and connections

Bijections
A bijection is both injective and surjective and has a two-sided inverse.
Video explanations to be added

Numbers and expressions

Number systems
Natural, integer, rational, real and complex numbers support progressively broader operations.
Video explanations to be added
Fractions and ratios
Fractions express quotients with nonzero denominators; ratios compare quantities with compatible units.
Video explanations to be added
Algebraic expressions
Expressions combine constants, variables and operations without necessarily asserting an equation.
Video explanations to be added
Polynomials
A polynomial is a finite sum of nonnegative integer powers with coefficients.
Video explanations to be added
Factorization
Factorization rewrites an expression as a product, helping locate zeros and simplify equations.
2 reviewed resources
Arithmetic operations
Addition, subtraction, multiplication and division follow precedence rules; division by zero is undefined.
Video explanations to be added
Percentages
A percentage expresses a ratio per hundred; percentage-point changes differ from relative percentage changes.
Video explanations to be added
Exponent laws
Power identities simplify products and quotients where bases and exponents satisfy the required domain conditions.
Video explanations to be added

Equations and inequalities

Linear equations
A one-variable linear equation has the form ax+b=0 with a nonzero for a unique solution.
Video explanations to be added
Quadratic equations
The discriminant determines the real-root structure of a quadratic with nonzero leading coefficient.
Video explanations to be added
Inequalities
Inequalities compare ordered values; multiplying by a negative number reverses the inequality.
Video explanations to be added
Absolute value
Absolute value measures distance from zero on the real line.
Video explanations to be added

Functions and growth

Functions
A function assigns exactly one output to each input in its domain; its domain matters when comparing expressions.
5 reviewed resources
Function composition
Composition applies one function after another where the output fits the next domain.
Video explanations to be added
Inverse functions
An inverse reverses a bijection; domain restrictions can make a function invertible.
Video explanations to be added
Exponential functions
An exponential with positive base other than one models multiplicative change.
Video explanations to be added
Logarithms
A logarithm is the inverse of an exponential, defined for positive arguments over the reals.
Video explanations to be added
Function transformations
Translations, scalings and reflections change a graph through controlled changes of its formula.
Video explanations to be added

Curriculum scope reference