Lecture 10: What is a Function, definition, piecewise defined
... • The set of numbers (or objects) to which we apply the function, A, is called the domain of the function. • The set of values of B which are equal to f (x) for some x in A is called the range of f . We have range of f = {f (x)|x ∈ A} In the example shown above where f (x) = x2 , we see that the va ...
... • The set of numbers (or objects) to which we apply the function, A, is called the domain of the function. • The set of values of B which are equal to f (x) for some x in A is called the range of f . We have range of f = {f (x)|x ∈ A} In the example shown above where f (x) = x2 , we see that the va ...
Excel Learning Sheet
... Attempt the following activities to develop your skills using a spreadsheet. You may find much of this is very applicable to your project. For assistance, you can learn about EXCEL functions by clicking the ’fx’ button/icon just over column C. Simulate Tossing a Coin Use Column A and B to show a ser ...
... Attempt the following activities to develop your skills using a spreadsheet. You may find much of this is very applicable to your project. For assistance, you can learn about EXCEL functions by clicking the ’fx’ button/icon just over column C. Simulate Tossing a Coin Use Column A and B to show a ser ...
Grade 6 Math Circles October 26, 2011 Introduction to Number Theory
... discover a method for finding perfect numbers. Firstly, you must start with 1 (20 ) and keep adding powers of 2 until the sum is a prime number (a number that is only divisible by one and itself). Once the prime number is attained, the perfect number is found by multiplying the sum and the last powe ...
... discover a method for finding perfect numbers. Firstly, you must start with 1 (20 ) and keep adding powers of 2 until the sum is a prime number (a number that is only divisible by one and itself). Once the prime number is attained, the perfect number is found by multiplying the sum and the last powe ...
Chap4 - Real Numbers
... Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the same cardinality or the sam ...
... Two sets M and N are equivalent … if it is possible to put them, by some law, in such a relation to one another that to every element of each one of them corresponds one and only one element of the other. If M and N are equivalent we often say that they have they have the same cardinality or the sam ...
Writing the Rule for an Arithmetic or Geometric Sequence
... d. t(n) = 5(1.2)n ; e. t(4) = 1620 An ordered list of numbers such as: 4, 9, 16, 25, 36, … creates a sequence. The numbers in the sequence are called terms. One way to identify and label terms is to use function notation. For example, if t(n) is the name of the sequence above, the first term is 4 an ...
... d. t(n) = 5(1.2)n ; e. t(4) = 1620 An ordered list of numbers such as: 4, 9, 16, 25, 36, … creates a sequence. The numbers in the sequence are called terms. One way to identify and label terms is to use function notation. For example, if t(n) is the name of the sequence above, the first term is 4 an ...
Alabama COS Standards
... 4. Analyze the graphs of rational, logarithmic, exponential, trigonometric, and piecewise-defined functions by determining the domain and range; identifying any vertical, horizontal, or oblique asymptotes; and classifying the function as increasing or decreasing, continuous or discontinuous, and not ...
... 4. Analyze the graphs of rational, logarithmic, exponential, trigonometric, and piecewise-defined functions by determining the domain and range; identifying any vertical, horizontal, or oblique asymptotes; and classifying the function as increasing or decreasing, continuous or discontinuous, and not ...
1 PROBLEM SET 8 DUE: Apr. 14 Problem 1 Let G, H, K be finitely
... the set of invariant divisors to the set of elementary divisors, and vice versa. (4). Determine all the abelian groups of order 1500 up to isomorphisms, and write down their elementary and invariant divisors. Problem 3 Show that a finite abelian p-group is generated by its elements of maximal order. ...
... the set of invariant divisors to the set of elementary divisors, and vice versa. (4). Determine all the abelian groups of order 1500 up to isomorphisms, and write down their elementary and invariant divisors. Problem 3 Show that a finite abelian p-group is generated by its elements of maximal order. ...
on numbers equal to the sum of two squares in
... squares. When is this true for this set of numbers? 2. Many natural numbers can be written as the sum of two squares in only one way. The first few numbers in this set are 2, 5, 8, 10, 13, … Now 10 = (12 + 12 )(12 + 2 2 ) , but the other numbers we listed cannot be expressed as a product of factors ...
... squares. When is this true for this set of numbers? 2. Many natural numbers can be written as the sum of two squares in only one way. The first few numbers in this set are 2, 5, 8, 10, 13, … Now 10 = (12 + 12 )(12 + 2 2 ) , but the other numbers we listed cannot be expressed as a product of factors ...
