what is a function in math

Let us learn about what is a function in math

A function f from N → N is referred by f(x) = 3x. Find the range of f.

Solution: f = {3, 6, 9, 12, …}

Given f(x) = 4x/(x +1) with domain (–3, –2, 0, 1, 3}. Find the range of f.

Solution: The range of f is (6, 8, 0, 2, 3}

A math function is a 1 of the type of relation. In a function, number two ordered pairs can have the same 1st element & a different 2nd element. That is, for functions, corresponding to every 1^st element of the ordered pairs, there must be a different 2^nd element. That is. In a function we can't have ordered pairs of the form (a₁, b₁) & (a₂, b₂) with a₁ = a₂ & b₁ ≠ b₂. It is called as function in math

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basic operations with polynomials

Let us learn about basic operations with polynomials

A polynomial is referred as a series of terms which are to be added to or subtracted from each other in an equation.

Best example of a trinomial would be 6x2-5x-6. For the ATC apprenticeship mathematics test you will work with factors to create polynomials.

A polynomial is referred as an algebraic expression in which the variables have non-negative integral exponents only.

Best example, all of the following expressions is polynomials:

17 + 2x + x2, x4 + 3x

The 1st & the last are polynomials in 1 variable x. The middle expression is a polynomial in 2 variables x & y. Therefore unless stated otherwise, polynomial will mean a polynomial in 1 variable. Operation of polynomials are classified following ways

a) Addition b) Subtraction c) Multiplication d) Division

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college algebra solver

Let us learn about college algebra solver

College algebra solver calculator reduces student homework time while teaching the concepts critical for success in Mathematics

College algebra solver is important Math equivalents & college algebra solver help to solve algebra word problems so as to make the interpretation of word problems easier.

Add = sum, total of, added to, together, increased by

Subtract =difference between, minus, less than, fewer than

Multiplication = of times, by a factor

Division = per, out of, ratio of, percent

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integration of exponential

Let us learn about integration of exponential


Integration of exponents is referred as the reverse process to differentiation. Integration is known as anti-differentiation. Integration of exponents is applied in many applications. Integration is applied to find the area between 2 curves & amount of work done, etc…Integration of exponential always deals with the exponential functions. Exponents are represented by the power of e. By differentiation of exponents you find the derivative of the mention exponential function, whereas by integration of exponential you find the exponential function whose derivative is called. This is known as the integration of exponential of the given exponential function.
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biconditional

Let us learn about biconditional

If 2 simple statements “p” & “q” are connected by the connective

'if & only if', then the resulting compound statement is known the biconditional statement. Symbolically biconditional is represented by p<-> q.

A biconditional is referred as a truth function which is true only in the case that both parameters are true or both are false.
Symbolically, the biconditional is written as aób or aób
The biconditional function is frequently written as ``iff,'' meaning ``if and only if.''
It gets its name from the fact that it is really 2 conditionals in conjunction,

(a->b)V (b->a)

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p value formula

Let us learn about p value formula

The p-value is referred as the area under the null distribution curve which is in bigger disagreement with the null hypothesis than the observed test statistics.
Best example, the hypothesis test for the mean is:

Imagine you have a large enough sample such that the central limit theorem holds & the mean is normally distributed then to test the null hypothesis H0: μ = Δ

find the test statistic “z” = (x Bar - Δ) / (sx / square root (n)) where “x” bar is the sample average
sx is the sample standard deviation
”n” is the sample size

The p value formula of the test is the area under the normal curve which is in agreement with the alternate hypothesis.

H1: μ > Δ; p-value is the area to the right of z
H1: μ < Δ; p-value is the area to the left of z
H1: μ ≠ Δ; p-value is the area in the tails is always greater than |z|

for a small test for the mean every thing is the same save the test statistic is a t statistic with n - 1 degrees of freedom. In such case the underlying distribution should be normal for this test to be valid.
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numerical coefficient

Let us learn about numerical coefficient
The definition for the numerical coefficient are given below the following section,

• Other name for the numerical coefficient is coefficient.

Best example, a₁ x₁ + a₂ x₂ + a₃ x₃ +……………………. a_n x_n
In the above given example,

• a₁ a₂ a₃ are known as numbers.
• x₁ x₂ x₃ are known as the variables.

Find the numerical coefficient for the product of mentioned terms, (2x² + 3x + 2) (x + 1).
The mentioned problem for numerical coefficient is,
(2x² + 3x + 2) (x + 1)
Next step, we have to product the above mentioned functions,
(2x² + 3x + 2) (x + 1)
= 2x² (x) + 3x(x) +2(x) +2x² + 3x + 2
= 2x³ + 3x² + 2x + 2x² + 3x + 2
= 2x³ + 5x² + 5x+2
Hence, the numerical coefficient is present before the variables.
Numerical coefficient = 2, 5, 5, 2
Thus, this is the required solution for the numerical coefficient.

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math dictionary algebra

Let us learn about math dictionary algebra

Math dictionary algebra is a branch of mathematics that deals in representing numbers through variables. math dictionary algebra also deals with symbols, relations, functions, and equations. Math dictionary algebra is a branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on 1 side of the scale with a number is also done to the other side of the scale. The numbers are the constants.

Math dictionary algebra is a very useful to everybody especially to students, tutors, researchers & etc. math dictionary algebra for students explains over 600 common mathematical terms & math words in simple language. The math dictionary algebra is much more than a compilation of words & definitions. Math dictionary algebra has been organized to reflect the different areas of mathematics taught in elementary & junior high schools. Within each category are all the terms commonly used in this field of math education, concise definitions, & many best examples & illustrations. In addition, the last chapter provides instructions for basic operations & tables of commonly-used facts & equivalents.

Math dictionary algebra may be used effectively in a variety of ways. Math dictionary algebra would definitely be an often sought reference book in any grade 4–9 math classroom, but it offers much more than simple definitions. Math dictionary algebra’s clear style & inclusion of many strategies for success in problem solving make it well adapted for independent instruction.

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permutations and combinations worksheet

Let us learn about permutations and combinations worksheet

In permutations without Repetition, you have to decrease the number of available selections every time. When you have n unlike things then you have to decrease one from the prior term for each time.
This is similar to n * (n-1) * (n-2)….
& if you are asked to select r things from n things, the combination is

n!

P (n, r) = ---------

(n-r)!

Combinations with Repetition for worksheet:
You require to do is change permutations formula to decrease it by how many customs the things could be in order but the order is not significant here.

n!

C (n, r) = ---------

r! (n-r)!

Combinations without Repetition for worksheet:
When you have n unlike things & to chose r things with repetition you have a formula

n+r-1

C (n, r) = -----------

r! (n-r)!

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factoring cubes

Let us learn about factoring cubes

The other 2 special factoring formulas are 2 sides of the same coin: the sum & difference of cubes. These are the formulas used.

a³ + b³ = (a + b)(a² – ab + b2)

a³ – b³ = (a – b)(a² + ab + b2)

The rule for factoring the sum of 2 perfect cubes is almost the same as the rule for factoring the difference between perfect cubes. To change 2 little signs to make it work. The sum of 2 cubes equal to the sum of its roots times the squares of its roots minus the product of the roots that looks like

a³ +b³ = (a+b) (a² –ab +b²)

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everyday math worksheets

Let us learn about everyday math worksheets
Everyday math worksheets make Student to learn better than is usually expected of them. Student comes to school knowing more than they currently get credit for. Mathematics refers more when it is rooted in real-life problems & situations.

Schools should take advantage of the tutoring tools which technology presents

Everyday math worksheets that help students practice graphing, arithmetic, telling time, handling money, & many more. Such activities are a great way to supplement student’s regular mathematics curriculum

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radical calculator

Let us learn about radical calculator

The radical calculator will reduce any number to its principal nth root as well as express it in simplest radical form. The radical of a positive integer “n” is referred as the product of the prime numbers dividing n:

The radical of any integer “n” is the biggest square free divisor of n, & so also described as the square-free kernel of “n” in mathematics.
Radical numbers for the 1st few positive integers are 1, 2, 3, 2, 5, 6, 7, 2, 3, 10, .The function radicals is to multiplicative in mathematics.
. Divide the given radicals : √16 / √4 = √16/ √2 = 4/2 = 2

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log laws

Let us learn about log laws

The "Laws" of Logarithms will allow you to change a single logarithm into the sum, difference, &/or production of logarithms. Logarithms is often easier to refer to the "Laws"

The natural logarithms written as:

log_ex or ln x

Where as e = 2.71828182846 base of natural logarithm

The natural logarithms are explained by the exponent of the power to that a base number must be raised to equal a given number. The solving natural logarithms are also said to be as the inverse of an exponent. In logarithm, it has 2 types of logarithms are the common logarithm, also said to be as the base 10 logarithms, & the natural logarithm, also said to be as the base e logarithm

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fraction reducer

Let us solve problem on fraction reducer

My pet dog is 1/4 years old and my dog is 7/4 years old find the total sums of ages & reducing the fractions
Solution:
Given pet is 1/4 years old
And my dog is 7/4 years old
Now we have to find the total sums of ages
= ¼ + 7/4
= 1 + 7/4
=8/4
By reducing the above fraction we get 2 is the solution
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ordinate abscissa

Let us learn about ordinate abscissa

Ordinate means the y-coordinate of a point: Ordinate’s distance from the x-axis measured parallel to the y-axis.
Abscissa means the x-coordinate of a point: Abscissa’s distance from the y-axis measured parallel to the x-axis.

The 1st element of the ordered pair is called Abscissa & the 2nd element of the ordered pair is called as the Ordinate. A simply X-coordinate point that is on the horizontal line is abscissa and Y-coordinate points on the vertical line are called as the Ordinate.

* Ordinate is said to be as the value of the Y-coordinate or Y-axis on a coordinate plane.

*Ordinate is said to be as the value of the vertical axis on a coordinate plane.

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probability worksheets elementary

Let us learn about probability worksheets elementary

Probability worksheet elementary is a branch of mathematics. Probability is a way of expressing knowledge or belief which is an event will occur or has occurred.

In mathematics the concept has been given an exact definition in probability theory which is used extensively in such areas of study as statistics, finance, mathematics, gambling, science, & philosophy to draw conclusions about the likelihood of potential events & the underlying mechanics of complex systems.

In math, the elementary probability is advance of converse or proposal an event will happen or occurred. The probability worksheet elementary is generally helpful to the study of the mathematics, gambling etc. The elementary math probability problems are performance of fluent familiarity or idea that happening will occur.

1. There are 3 red color balls, & six blue color balls. Then you will select the balls without looking & then put it back. You can do this action for 9 times. Find the best prediction possible for the number of times that you will pick a blue ball.
Solution: There are 9 balls, so the possible out comes is 9.
The number of blue color balls is 6. So, the possible outcomes to pick blue color ball is 6.
The probability = 6 out of 9 or 6/9
You will find 6/9 of 9
6/9 x 9 = 6 The best prediction = 6 out of 9 times Answer: 6 times.
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