Free Online Tutorials on Functions and Algebra
Free analytical Tutorials using step by step approach with examples and matched exercises are presented here. Detailed solutions to the examples are also included. Several tutorials have been designed so that they can be used with the applets tutorials in this site.
Applications, Graphs, Domain and Range of Functions
Algebra
Lines
-
Slopes of Perpendicular Lines Questions. A detailed tutorial on proof that the slope of two parallel lines are equal and also questions with detailed solution.
-
Slopes of Perpendicular Lines Questions. 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 and also questions with detailed solutions.
Exponential and Logarithmic Functions and Equations
Quadratic Functions Problems
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
-
Polynomial Division. The long division process of Polynomials is presented using an example.
- Synthetic Polynomial Division.
- Applications of Synthetic Polynomial Division.
l
- Online Polynomial Division Calculator.
- Introduction to Polynomials. Definition of degree, leading coefficient, monomial, binomial, trinomial and constant, linear, quadratic and cubic polynomial.
- Add, Subtract and simplify 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
- Graphs of Polynomials Functions
- Graphs of Second Degree Polynomials. The graphs of several second degree polynomials are shown along with questions and answers.
- Graphs of Third Degree Polynomials. The graphs of several third degree polynomials are shown along with questions and answers.
Rational Functions
Circle, Ellipse, Parabola and Hyperbola Equations
Find Inverse Functions
Composition of Functions
Numbers
Fractions
Percentages
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
Determinant of a Matrix and Cramer's rule
Rational Expressions
Absolute Value
Slopes and Lines