Free Online Tutorials on Functions and Algebra

Applications, Graphs, Domain and Range of Functions

• Applications of Functions. Several problems and exercises to illustrate possible applications of functions.



• Applications and Use of the Inverse Functions. Examples on how to apply and use inverse functions in real life situations and solve problems in mathematics.



• Graphs of Functions - Tutorials. Identify the graph of an algebraic function given by its formula.



• domain and range of basic functions. A table of domain and range of basic and useful functions.



• Domain and Range of Functions and the Answers to matched problems 1,2,3 and 4. Tutorial, with detailed solutions, on how to find the domain and range of real valued functions.



• Evaluate Functions. Tutorial on how to find the value of a function using its formula.



• x and y Intercepts Of Graphs. How to determine the x and the y intercepts of the graphs of functions? Examples with detailed solutions.



• How to Find Zeros of a Function?. How to find the zeros of functions; tutorial with examples and detailed solutions.



• Questions on one to one Functions. Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function.

Algebra

• Algebra Tutorial and the detailed solutions to the matched problems.



• Basic Rules and Properties of Algebra. Rules and Properties such as commutativity, associativity and distributivity of algebra with examples.



• Mathematical Induction - Problems With Solutions. Several problems, with detailed solutions, on mathematical induction are presented.

Lines

• Prove That the Slopes of Two Parallel Lines Are Equal. Detailed solution.



• Slopes of Two Perpendicular Lines. A detailed tutorial on the proof of the fact that two perpendicular lines have slopes such that one is the negative of the reciprocal of the other.

Exponential and Logarithmic Functions

• Tutorial on exponential functions (1).. Tutorial, with examples and detailed solutions, on exponential functions.



• Tutorial on exponential functions (2) - Problems. Solve problems involving exponential functions.



• Exponential and Logarithmic Equations. A tutorial, with examples and detailed solutions, on logarithmic and exponential equations.



• Tutorial on logarithmic functions.. Tutorial on logarithmic functions with detailed solutions of examples.



• Convert Logarithms and Exponentials.. Tutorial, with examples, on the conversion of logarithmic expression into exponentials and vice versa is.

Quadratic Functions

• Vertex and Intercepts Parabola Problems . Problems, with detailed solutions, involving quadratic functions, parabola, vertex and intercepts..
  
  
• Quadratic Functions - Problem (1). . Solve problems involving quadratic functions.
  
  
• Tutorial on quadratic functions with answers matched exercises.

Floor and Ceiling Functions

• Floor Function. The floor function floor(x) is defined as the function that gives the highest integer less than or equal to x.
  
  
• Ceiling Function. The ceiling function ceiling(x) is defined as the function that gives the smallest integer greater than or equal to x.

Polynomial Functions

• Introduction to Polynomials. Definition of monomial, binomial, trinomial and polynomial.



• Add and Subtract Polynomials. A detailed tutorial on what are like terms, how to group them and how to add and subtract polynomials.



• Factor Polynomials. Tutorial, with detailed solutions, on factoring polynomials



• Polynomial Functions, Zeros, Factors and Intercepts. Find polynomial functions given their zeros, graphs and some other information.



• Find Zeros of Polynomial Functions - Problems

Rational Functions

• Tutorial on rational functions and answers to the matched exercises.



• Graphs of Rational Functions - Tutorials. Identify graphs of rational functions.

Circle, Ellipse and Hyperbola Equations

• Tutorial on Equation of Circle and the answers to the matched exercises: Find equation of a circle, radius and center.



• Tutorial on equation of circle(2) and the answers to the matched exercises: Find equation of the circle.



• Tutorial on equation of circle(3). Find the equation of the circle.



• Ellipse Problems. Problems related to the ellipse equation.



• Hyperbola Problems. Problems with detailed solutions on the hyperbola equation.

Find Inverse Functions

• Properties of Inverse Functions. Tutorial on the properties of inverse functions with some examples.
  
  
• Find inverse function (1)- Tutorial. Find inverse functions analytically.



• Find inverse function (2)- Tutorial. Find inverse functions analytically.



• Inverse of Quadratic Functions. Examples with detailed solutions on how to find the inverse of quadratic functions with restricted domains.

Composition of Functions

• Composition of Functions. Find the composition of functions and its domain.

Numbers

• Prime Factors. Several examples with detailed solutions on how to factor a positive integer using prime numbers.
  
  
• Even and Odd Numbers Problems. Problems with detailed solutions and exercises on even and odd numbers.
  
  
• Divisibilty Tests of Whole Numbers. How to test a whole number for divisibility by 2, 3, 4, 5, 6, 8, 9 and 10.
  
  
• Divisibilty Questions With Solutions. Tutorials with SAT math test like questions and their detailed solutions on divisibility.

Fractions

• interactive tutorial on fractions Explore fractions interactively using an applet.
  
  
• interactive tutorial on equivalent fractions Explore equivalent fractions interactively using an applet.
  
  
• Add Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises.
  
  
• Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.
  
  
• Divide Fractions. Divide a fraction by a fraction, a fraction by a number of a number by a fraction. Several examples with solutions and exercises with answers.

Percentages

• Interactive Tutorial on Percentage Interactive tutorial on percentages using an applet.
  
  
• Percent Math Problems Several word problems on percentage with detailed solutions are presented.
  
  
• Percent Math Questions Several questions on percentages, with detailed solutions are presented.
  
  
• Convert Percentages, Fractions and Decimals Tutorial on how to convert percentages, fractions and decimals. Questions with detailed solutions as well as exercises with answers are presented.
  
  

Vectors

• Vector Addition and Scalar Multiplication. A tutorial on how to find components of a vector , add two vectors, multiply a vector by a scalar. Examples, solutions, exercises and answers are included.
  
  
• Dot Product of Two Vectors and Applications. A tutorial on the dot product of two vectors and how it is applied to find angle between two vectors.

Matrices

• Matrix Addition and Multiplication. A tutorial on how to add, multiply by a scalar and multiply matrices with examples, solutions, exercises and answers.
  
  
• The Inverse of a Square Matrix. A tutorial on how to find the inverse of any square matrix. The proof of a formula that gives the inverse of an invertible 2 x 2 matrix is also included.

Complex Numbers

• Complex Numbers - Basic Operations. A tutorial on how to find the conjugate of a complex number and add, subtract, multiply, divide complex numbers supported by online calculators.

Determinant of a Matrix and Cramer's rule

• Calculate Determinant of a Matrix. A tutorial to calculate the determinant of 2 by 2 and 3 by 3 matrices.
  
  
• Cramer's Rule to Solve Systems of Equations. A tutorial on proving Cramer's rule for a 2 by 2 systems of linear equations. Presentation of the rule for a 3 by 3 systems of equations. An example on using Cramer's rule is presented.

Rational Expressions

• Rational Expressions. Define rational expressions and their domains.
  
  
• Simplify Rational Expressions. Tutorial on how to simplify rational expressions.

Absolute Value

• Simplify Absolute Value Expressions. Tutorial on how to simplify expressions with absolute value.

Solve Equations, Systems of Equations and Inequalities

Slopes and Lines

• Slope of a line and detailed solutions to matched exercises in the tutorial.



• Equations of Lines in Different Forms
. Tutorial on the different forms of the equations of lines.


• Equation of a line
. Tutorial on how to find the slopes and equations of lines.