What Does Function Of Mean
Annotation category:Chapter 3
Note: 
A function defines one variable in terms of another. The statement “y is a function of x” ) means that y varies according to whatever value x takes on. A causal relationship is often implied , but does not *necessarily* exist.
The number of hours you spend toiling away in Butler library may be a function of the number of classes you’re taking. It’s also likely to be a function of whether you have a computer in your dorm room, whether you have a printer in your dorm room, and whether your roommates are loud and obnoxious and won’t let you study.
In turn, the number of classes you’re taking may be a function of your major. It is also likely to be a function of how many extracurricular activities you participate in, how much sleep you need, and how crazy you are.
Knowing that one variable somehow changes with another is a starting point. Uncovering the specific nature of their relationship is another, and in science it is vital to understanding how systems behave. Such work can become a complicated business. Fortunately we have access to a language which, although it may have earned the undeserved reputation of being hopelessly complex, is actually the simplest, most efficient way to solve these problems. So let’s do some translating:
If y = 2x, that means that for every incremental increase in x, y increases by 2 increments. Y is twice the value of x, for every value x takes on.
If x = 5, then y = 2 x 5 = 10.
so that y = 365x + x/4 + b.
Writing An Equation In The Slope Intercept Form
If the slope ‘m’ and yintercept ‘b’ are given, then the equation of the straight line can be written in the form of ‘y = mx +b’. For example, if the slope for a line is 2 and the yintercept ‘b’ is 1, then the equation of the straight line is written as y = 2x – 1. The slope value can be positive or negative. As we discussed in the earlier sections, in y = mx + b, ‘m’ represents the slope of the equation. To find the slope of a line, given its equation, we have to rearrange its terms to the slopeintercept form y = mx + b. Here, ‘m’ gives the slope and ‘b’ gives the yintercept of the equation.
Let us consider the equation 2x + 3y = 6. We are required to find the slope and the yintercept from the equation which is of the form Ax + By = C
We rewrite the standard form of the equation of the line to the slopeintercept form y = mx + b.
2x + 3y = 63y = 2x + 6y = x + 2
Comparing the final equation with y = mx + b, we obtain the slope of the equation is m = 2/3 and the yintercept of the equation is, b = 2 or .
Important Notes:
 The equation of the slopeintercept form of a line whose slope is ‘m’ and whose yintercept is ‘b’ or is y = mx + b.
 The equation of a horizontal line passing through is of the form y = b.
 The equation of a vertical line passing through is of the form x = a.
 m is calculated using the formula rise over run or /
What Is The Difference Between And
means provableBut is used exactly the same:
A B ¬B ¬A A B ¬B ¬A
Can you present a good example where they are different? Is it like the incompleteness theorem of recursive sets that there are sentences that are true i.e. but do not have the property i.e. provable?
Thanks for any insight
$A \models B$ means that $B$ is true in every structure in which $A$ is true. $A\vdash B$ means $B$ can be proved using $A$ as the premises.
Firstorder logic simultaneously enjoys the following properties: There is a system of proof for which
 If $A\vdash B$ then $A\models B$
 If $A\models B$ then $A\vdash B$
 There is a proofchecking algorithm .
That last point is in stark contrast to this fact: There is no provabilitychecking algorithm. You can search for a proof of a firstorder formula in such a systematic way that you’ll find it if it exists, and you’ll search forever if it doesn’t. But if you’ve been searching for a million years and it hasn’t turned up yet, you don’t know whether the search will go on forever or end next week. These are results proved in the 1930s. The nonexistence of an algorithm for deciding whether a formula is provable is called Church’s theorem, after Alonzo Church.
I learned that $\models$ stands for semantic entailment, while $\vdash$ stands for provability in a certain proof system.
Michael Hardy and Johannes Kloos have answered this already, but I thought a typical example might illuminate the point further. $\def\ra$
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Four Ways To Represent A Function
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 4434
 Determine whether a relation represents a function.
 Find the value of a function.
 Determine whether a function is onetoone.
 Use the vertical line test to identify functions.
 Graph the functions listed in the library of functions.
A jetliner changes altitude as its distance from the starting point of a flight increases. The weight of a growing child increases with time. In each case, one quantity depends on another. There is a relationship between the two quantities that we can describe, analyze, and use to make predictions. In this section, we will analyze such relationships.
How Do You Calculate Conditional Expectations
The conditional expectation, E, is a number depending on y. If Y has an influence on the value of X, then Y will have an influence on the average value of X. So, for example, we would expect E to be different from E.
How do you find the expectation of a Poisson distribution?
The expected value of the Poisson distribution is given as follows: E = = d)/dt, at t=1. Therefore, the expected value and the variance of the Poisson distribution is equal to .
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Meaning Of Y = Mx + B
y = mx + b is the slopeintercept form of a staight line. In the equation y = mx + b for a straight line, m is called the slope of the line and b is the yintercept of a line. y = mx+b, where
y how far up or down is the line,
x how far along is the line,
b the value of y when x = 0 and
m how steep the line is.
This is determined by m = / . Note that difference in y coordinates is indicated as rise or fall and difference in x coordinates is indicated as run.
Math Symbols Used In Logic
The following table shows the math symbols used in logic.
Symbols  

There exists at least one 
x: P x: F There exists at least one element of p, \, such that F is True. 

\  There exists one and only one 
! x: F means that there is exactly one \ such that F is true. 
\  \  
\  Statement A is true only if \ is false\\)  
\ 
The statement A \ B is true if A or B is true if both are false, 

The statement A \ B is true if A and B are both true else it is false. 

x +1 = y +1 \ x = y  
\ or \ 
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What Do The Letters R Q N And Z Mean In Math
In math, the letters R, Q, N, and Z refer, respectively, to real numbers, rational numbers, natural numbers, and integers.
Who are the experts?Our certified Educators are real professors, teachers, and scholars who use their academic expertise to tackle your toughest questions. Educators go through a rigorous application process, and every answer they submit is reviewed by our inhouse editorial team.
The letters R, Q, N, and Z refers to a set of numbers such that:
R = real numbers includes all real number
Q= rational numbers
N = Natural numbers
z = integers ( all integers…
What Does This Symbol Mean In Math
In comparison to. This sign denotes less than for example, 2 denotes more than. 4 > 2. These symbols are often used in mathematics and signify less than or equal to and greater than or equal to. => = is used in computer applications.What does F X > mean?f simply means y, while f’ generally implies dy/dx. If x has a value, such as f = 2x + 1, then f equals 3.
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Using The Vertical Line Test
As we have seen in some examples above, we can represent a function using a graph. Graphs display a great many inputoutput pairs in a small space. The visual information they provide often makes relationships easier to understand. By convention, graphs are typically constructed with the input values along the horizontal axis and the output values along the vertical axis.
The most common graphs name the input value \ and the output \, and we say \ is a function of \, or \\) when the function is named \. The graph of the function is the set of all points \\) in the plane that satisfies the equation \\). If the function is defined for only a few input values, then the graph of the function is only a few points, where the xcoordinate of each point is an input value and the ycoordinate of each point is the corresponding output value. For example, the black dots on the graph in Figure \ tell us that \=2\) and \=1\). However, the set of all points \\) satisfying \\) is a curve. The curve shown includes \\) and \\) because the curve passes through those points
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value. See Figure \.
Howto: Given a graph, use the vertical line test to determine if the graph represents a function
Example \: Applying the Vertical Line Test
Positive Numbers Negative Numbers
Real numbers whose graphs are to the right of 0 are called positive real numbers, or more simply, positive numbers. Real numbers whose graphs appear to the left of 0 are called negative real numbers, or negative numbers.
The number 0 is neither positive nor negative.
Watch the video for a simple explanation of positive and negative numbers on a real number line. 
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What Does E Mean In Math
The letter E can have two different meaning in math, depending on whether it’s a capital E or a lowercase e. You usually see the capital E on a calculator, where it means to raise the number that comes after it to a power of 10. For example, 1E6 would stand for 1 × 106, or 1 million. Normally, the use of E is reserved for numbers that would be too long to be displayed on the calculator screen if they were written out longhand.
Mathematicians use the lowercase e for a much more interesting purpose to denote Euler’s number. This number, like , is an irrational number, because it has a nonrecurring decimal that stretches to infinity. Like an irrational person, an irrational number seems to make no sense, but the number that e denotes doesn’t have to make sense to be useful. In fact, it’s one of the most useful numbers in mathematics.
What Is Y Intercept
The y intercept of a graph is the point where the graph intersects the yaxis. We know that the xcoordinate of any point on the yaxis is 0. So the xcoordinate of a yintercept is 0.
Here is an example of a yintercept. Consider the line y = x+ 3. This graph meets the yaxis at the point . Thus is the yintercept of the line y = x+ 3.
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How To Find Y
We have derived the formulas to find the yintercept of a line where the equation of the straight line is in different forms. In fact, we do not need to apply any of these formulas to find the yintercept of a straight line. The yintercept of the polynomial function of the form y = a1xn + a2 xn1+ … + an is just its constant term an .
We just substitute x=0 in the equation of the line and solve for y. Then the corresponding yintercept is y or .
Equation of Line  

y=23=3  3 
The yintercept of a function can be easily found by graphing it using the graphing calculator and locating the point where the graph cuts the yaxis. A function has only one yintercept because otherwise, it fails the vertical line test. The yintercept of the second equation of the table is shown in the graph below.
Representing Functions Using Tables
A common method of representing functions is in the form of a table. The table rows or columns display the corresponding input and output values. In some cases, these values represent all we know about the relationship other times, the table provides a few select examples from a more complete relationship.
Table \ lists the input number of each month , \, and so on) and the output value of the number of days in that month. This information represents all we know about the months and days for a given year . Note that, in this table, we define a daysinamonth function \ where \\) identifies months by an integer rather than by name.
Table \: Months and number of days per month.Month number, \ 
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How Do I Construct A Real Number Line
Here are three steps to follow to create a real number line.
Choose any point on the line and label it 0. This point is called the origin.
Now that you have created a number line, it is time see how points on a number line are defined.
Real Numbers
A real number is any number that is the coordinate of a point on the real number line.
E In Scientific Notation And The Meaning Of 1e6
You don’t need a calculator to use E to express a number in scientific notation. You can simply let E stand for the base root of an exponent, but only when the base is 10. You wouldn’t use E to stand for base 8, 4 or any other base, especially if the base is Euler’s number, e.
When you use E in this way, you write the number xEy, where x is the first set of integers in the number and y is the exponent. For example, you would write the number 1 million as 1E6. In regular scientific notation, this is 1 × 106, or 1 followed by 6 zeros. Similarly 5 million would be 5E6, and 42,732 would be 4.27E4. When writing a number in scientific notation, whether you use E or not, you usually round to two decimal places.
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What Does Y Mean In Math
What does y mean in Math?
In math, y is generally used as an unknown variable. we use y as a variable just like x .
x is also used as a variable in Algebra
y holds the place of a number that we may not know just yet in prealgebra. We use this symbol when we dont know how many we have of something or when the number of them can change.
y + 4 means we add 4 to whatever we decide y stands for. y could be any number, so were just holding its place with the variable
Evaluating Functions Expressed In Formulas
Some functions are defined by mathematical rules or procedures expressed in equation form. If it is possible to express the function output with a formula involving the input quantity, then we can define a function in algebraic form. For example, the equation \ expresses a functional relationship between \ and \. We can rewrite it to decide if \ is a function of \.
How to: Given a function in equation form, write its algebraic formula.
Example \: Finding an Equation of a Function
Express the relationship \ as a function \\), if possible.
Solution
To express the relationship in this form, we need to be able to write the relationship where \ is a function of \, which means writing it as \.
Therefore, \ as a function of \ is written as
Analysis
It is important to note that not every relationship expressed by an equation can also be expressed as a function with a formula.
Example \: Expressing the Equation of a Circle as a Function
Does the equation \ represent a function with \ as input and \ as output? If so, express the relationship as a function \\).
Solution

\=\dfrac}\)
Q & A
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