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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