5 Questions
What is the purpose of decomposition of a rational function?
To simplify the function
The modulus function is an example of a signum function.
False
A _______________________ is a function that assigns to each real number $x$ the largest integer less than or equal to $x$.
Greatest Integer function
What is the purpose of finding the inverse of a square matrix?
To solve systems of linear equations
Match the following concepts with their corresponding units:
Frequency distribution = Unit Five Matrices = Unit Six Modulus function = Unit One Permutation = Unit Five
Study Notes
Unit One: Relations and Functions
- Revision of relations includes understanding the concept of inverse of a relation.
- A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
- Modulus function: a function that returns the absolute value of a number.
- Signum function: a function that returns -1 if the input is negative, 0 if the input is zero, and 1 if the input is positive.
- Greatest Integer function: a function that returns the largest integer less than or equal to the input.
Classification of Functions
- Functions can be classified as injective, surjective, bijective, and composite functions.
Unit Two: Rational Functions
- Simplification of rational functions involves cancelling out common factors between the numerator and denominator.
- Decomposition of rational functions involves breaking down a rational function into simpler fractions.
- Graph of rational function: a visual representation of the relationship between the input and output of a rational function.
Unit Five: Statistics and Probability
- Frequency distribution: a table that displays the frequency of each value in a dataset.
- Measure of location: includes mean, median, and mode.
- Quartile, decile, and percentile: measures of position that divide a dataset into parts.
- Permutation: an arrangement of objects in a specific order.
- Combination: a selection of objects without regard to order.
- Probability: a measure of the likelihood of an event occurring.
Unit Six: Matrices and Determinants
- Matrices: rectangular arrays of numbers, symbols, or expressions.
- Determinant: a scalar value that can be computed from the elements of a matrix.
- Inverse of a square matrix: a matrix that when multiplied by the original matrix, results in the identity matrix.
- Systems of linear equations can be solved using matrices and determinants.
Unit Seven: Vectors and Transformations
- Vectors: quantities with magnitude and direction.
- Scalars: quantities with magnitude only.
- Transformation of the plane: a change in the position or orientation of the plane, which can be represented using vectors and matrices.
Review of relations and functions, including inverse of a relation, domain, range, modulus, signum, and greatest integer functions.
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