all functions are relations but why not all relations are functions​

Answers

Answer 1

Answer:

All functions are relations, but not all relations are functions. A function is a relation that for each input, there is only one output. Here are mappings of functions. The domain is the input or the x-value, and the range is the output, or the y-value.

Answer 2

Answer:

Step-by-step explanation:

A relation between members of two sets X and Y is any set of ordered pairs {(x1,y1) (x2,y2) … }, finite or infinite in their number, provided the first member is from X and the second member is from Y. (Let’s not mention the uncountable possibility here).

E.g., if X = {Sunday, Monday, …, Saturday} and Y = {1,2, …, 31}, then the set {(Monday,1) (Tuesday,2) … (Monday,8) (Tuesday,9) … (Sunday,28)} is a useful relation for some February calendar, somewhere. It is “one-to-many”. And note that set Y need not be covered, but X must be. This distinguishes the domain of the relation (days of the week here) from its codomain (whole numbers 1 to 31 here).

Considering the vast set of all relations, there is one subset of great importance, those relations that have unique codomain values for each domain value. That is, each x in X is paired unambiguously with exactly one y in Y. These special relations are functions. The set of y in Y which have been paired with some x in X is called the range of f. Functions may still be “many-to-one”, as in y = r(x) which gives x rounded to the nearest integer. Thus r(2.3) = r(1.9) = 2.

Within the subset of functions are the one-to-one functions, which also have the property that every y in the range is paired with exactly one x in the domain. Because of this, these are the only functions that have an inverse function. Thus, the inverse function can be written as {(y1,x1) (y2,x2) … }. This shows that the domain and range of the original function are exactly exchanged in the inverse function.

E.g., y = tan(x) is one-to-one with domain [-pi/4 , pi/4] and range [-1,1]. Its inverse is x = arctan(y) with domain [-1,1] and range [-pi/4 , pi/4]. The roles of x and y are unambiguous, and shouldn’t be exchanged: x always in [-pi/4 , pi/4] and y always in [-1,1].


Related Questions

PLEASE HELP!! I NEED THESE BONUS POINTS!! If you do answer plz answer all of them. Thank you! I will choose brainiest ;)

Answers

Answer:

7-9 you need to plug numbers into the formula y= mx+b where you plug the plots in M and B.

Step-by-step explanation:

I don't have a graph to plot 1-3 on but all you need to do is plot them and answer if they are parallel, perpendicular, or neither. (The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.) (In math, parallel means two lines that never intersect — think of an equal sign.) And if they don't fit either then its NEITHER

this problem makes me wanna cry

Answers

Answer:

k=45

Step-by-step explanation:

its an isosceles triangle, so k=45

to check it, 45+45+90=180

can someone please help me

Answers

Answer:

18=2x+7, The internship pays $5.50 an hour.

Step-by-step explanation:

The box on the far left is the amount the student is paid at their job, which is $18 an hour in this case. Solve 18-7 to get 11, then divide 11 by 2 to get the pay for the internship. To check your work, plug 5.50 into the equation.

18=2(5.50)+7

18=11+7

18=18

Answer:

The equation would be:

18 = 2x + 7

The internship pays $5.5 an hour

Step-by-step explanation:

18 - 7 = 2x

(Since we moved the 7 to the other side, in order to combine like terms)

11 = 2x

(Divide both sides by 2)

5.5 = x

(x = 5.5)

x would be the pay the internship pays an hour.

(Sorry if this is wrong, notify me if it is, and I'll delete this post Xc)

how do you write 2/11 as a decimal using long division​

Answers

Answer:

0.18

Step-by-step explanation: Converting the fraction 2/11 into a decimal is very easy. To get 2/11 converted to decimal, you simply divide 2 by 11.

Answer:

About 0.18

Step-by-step explanation:

Divide 2 by 11

A particular shade of orange paint has 2 cups of yellow paint for every 3 cups of red paint.According to the double number line, how many cups of red paint are required to make three batches

Answers

Answer:9 cups of red paint

Step-by-step explanation:1 batch = 3 cups of paint and you need to find the number of cups of paint for 3 batches so you multiply 3 x 3 and get 9. Hope this helped!!!:)

the set of types of matter
well difined or not​

Answers

Answer:

It is not well defined.

Step-by-step explanation:

Because set is a collection of well defined objet. And matter contains of solid, liquid and gas

What distribution of clothing should Nancy have for German males and females? Should she produce more small or large sizes, or should she have an even distribution of all sizes?

Answers

Answer: I sacrificed my answer for yours here u go love

Step-by-step explanation:

Nancy should produce more large sizes of the male clothing for German men since the data is skewed left, meaning there are more data values that lie on the right side, representing taller males. For women, she can have a roughly even distribution of sizes since the data set is symmetric.

Nancy should produce more large sizes of the male clothing for German men and for women, she can have a roughly even distribution of sizes since the data set is symmetric.

What is skewness in histogram?Skewness is the tendency for the values to be more frequent around the high or low ends of the x-axis.Skewness is the measure of the asymmetry of a histogram (frequency distribution). A histogram with normal distribution is symmetrical.

Given is to find what distribution of clothing should Nancy have for German males and females.

The shape of the data for German male adult heights is skewed left, but the shape of the data for female adult heights is close to symmetric. So, the distribution of the data is not the same. Each data set has the same minimum height of 145 centimeters. However, the maximum male adult height is 220 centimeters and the maximum female height is 185 centimeters. So, the range of values is not the same. The data for male adult heights has an outlier, but the data for female adult heights doesn't have any outliers.

Nancy should produce more large sizes of the male clothing for German men since the data is skewed left, meaning there are more data values that lie on the right side, representing taller males. For women, she can have a roughly even distribution of sizes since the data set is symmetric.

Therefore, Nancy should produce more large sizes of the male clothing for German men and for women, she can have a roughly even distribution of sizes since the data set is symmetric.

To solve more questions on skewness, visit the link below -

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Find the equation of the line from the following graph in slope-intercept form:
A) y = 3/2x + 2
B) y = -3/2x + 2
C) y = -2/3x + 2
D) y = 2/3x + 2

Answers

Answer: the slope is -3/2x and B is the only one that SLOPE

Step-by-step explanation:

RISE/RUN

IT WENT UP 3 AND WENT 2 TO THE LEFT

BTW: TO THE LEFT IS NEG AND POS IT TO THE RIGHT

so the slope is a neg be it is going toe the up towards left

please help need asap

Answers

Answer:

b and e.

Step-by-step explanation:

You will find this by solving each equation for 15b (get 15b by itself)

Question
1 pts
I bought a new bike! It was originally $600 but I had a 25% coupon. What
was the discount?
O $25
O $150
O $450
$1000
Question 3
1 pts
I NEED THIS DONE ASAP

Answers

Answer:

b or 150

Step-by-step explanation:


The classroom has 10 desks with boys and
girls. Show one combination of boys and
girls

Answers

Answer:

one combination could be 6 girls and 4 boys

3(2x - 7) = 5(x + 3) + 2x7​

Answers

That would equal to 50 or x=50

Answer:

x = -1.52016

Step-by-step explanation:

Step 1: Write equation

3(2x - 7) = 5(x + 3) + 2x⁷

Step 2: Solve for x

Distribute: 6x - 21 = 5x + 15 + 2x⁷Subtract 6x on both sides: -21 = -x + 15 + 2x⁷Add 21 to both sides: 0 = -x + 36 + 2x⁷Rearrange: 0 = 2x⁷ - x + 36Find roots by graphing: x = -1.52016

Need some help please...

Answers

Answer:

C: Starting at 1103 you gain 91 feet each additional hour of climing.

Step-by-step explanation:

What is the equation in slope-intercept form of the line that passes through the points ( -4, 47) and ( 2 , -16)?

A) y= -
21
2
x +
979
21

B) y= -
2
21
x +
979
21

C) y= -
21
2
x + 5

D) y= -
2
21
x +5

Answers

Answer:c

Step-by-step explanation:

Which are irrational and which are rational ?

Answers

Answer: 8/9 is rational

.2593 irrational

square root of 7: irrational

square root of .25 is rational

square root of 14: irrational

0 is a: rational

square root of 280: irrational

square root of 35: is irrational

.2222: is rational

square root of 3r is a rational number......

Step-by-step explanation:

Tien Chou's tax return for last year shows a total tax of $8,278. Tien's employer withheld $8,450 from her wages during the year. What refund should Tien receive

Answers

Answer: 16,728

Step-by-step explanation:

Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-1, -6), B(-1,7), C(1, 7), and D(1, -6). Given these coordinates, what is the length of side AB of this rectangle?

Answers

Answer:

13

A(-1, -6), B(-1,7)

7-(-6)=13

Answer:

13

Step-by-step explanation:

3(y – 5) + 2 = 5
A. y = 4
B. y = 7
C. y = –4
D. y = 6

Answers

Answer:

y = 6

Step-by-step explanation:

Step 1: Write equation

3(y - 5) + 2 = 5

Step 2: Solve for y

Distribute 3: 3y - 15 + 2 = 5Combine like terms: 3y - 13 = 5Add 13 to both sides: 3y = 18Divide both sides by 3: y = 6

Step 3: Check

Plug in y to verify it's a solution.

3(6 - 5) + 2 = 5

3(1) + 2 = 5

3 + 2 = 5

5 = 5

6
Directions - Determine the correlation for the situation. Choose Positive/ Negative/ or No correlation for each.
The outside temperature in the summer and the cost of the electric bill (for air conditioning).
A) Positive correlation
B Negative correlation
No Correlation

Answers

Probably No correlation because they don't relate to each other

As the temperature in the summer goes up, so does the cost to supply cooling to the house (the AC has to work harder due to higher level of heat)

A is correct - they both increase and decrease together

A ball held 2.0 meters above the floor has 59 joules of potential energy. The ball’s mass
the answer3

Answers

Answer:

Step-by-step explanation:

potential energy=mgh

59=m×9.8×2

19.6 m=59m=59/19.6≈3.01 gram

the length of each side of this regular pentagon is 37 mm. what is the perimeter

Answers

Answer:

185mm

Step-by-step explanation:

37 times 5 is 185

Answer:

185 mm

Step-by-step explanation:

There are 5 sides in a pentagon. Each side is 37 mm. Add 37 5 times or multiply 37 by 5.

37mm + 37mm + 37mm + 37mm + 37mm

or

37mm × 5

Solving systems by substitution

Answers

Tank 1: v = 1540 - 6m

Tank 2: v = 236 + 6m

109 minutes, less than two hours, since two hours is 120 minutes (60 minutes in one hour, times 2)

Set them equal to each other to find out when they will have the same number of gallons: 1540 - 6m = 236 + 6m

1304 = 12m
108.667 rounded to the nearest minute is 109 minutes, which is the answer.

what is the midpoint of (-9, -4) and (-6, -3) ?

A (-3, -2)
B (3, 2)
C (-3, 12)
D (-12, -5)

Answers

Answer: c hope this helps

11.0453610171873

Midpoint

(−6.5,3.5)

Slope

11

x intercept

−6.82

y intercept

75.00

Step-by-step explanation:

30 pts! Will make brainliest
Ben tracked the attendance in his class over a period of time and recorded the data in a frequency table.

Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots

Answers

The data recorded by Ben shows the attendance log of his classmates over a given period of time.

What is a Dot Plot?

This refers to a simple chart that resembles a histogram that is used to represent small data.

Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,

Read more about dot plots here:

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Answer: took the

Step-by-step explanation:

Lena says that and are like terms. Is she correct? Why or why not? A. No, because the same variables are not raised to the same powers. B. Yes, because both terms have a variable with a power of 3 and a power of 1. C. Yes, because both terms have an x and a y. D. No, because the two terms do not have the same coefficients.

Answers

Answer:

D because of the question

No, because the same variables are not raised to the same powers. which is the correct answer would be an option (A).

What is a polynomial?

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

Lena says that 4xy³ and -5x³y are like terms

⇒ 4xy³ and -5x³y

Here both polynomials are not like terms, because the same variables are not raised to the same powers.

Therefore, the correct answer would be an option (A).

Learn more about the polynomial here:

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The question seems to be incomplete the correct question would be

Lena says that 4xy³ and -5x³y are like terms. Is she correct? Why or why not?

How to solve (x-10)(x + 10)

Answers

Answer:

x² - 100

Step-by-step explanation:

Use the FOIL method. The FOIL method is the way in which you multiply the terms:

FOIL stands for First, Outside, Inside, Last. Multiply:

First:

x * x = x²

Outside:

x * 10 = 10x

Inside:

-10 * x = -10x

Last:

-10 * 10 = -100

Combine like terms:

x² + 10x - 10x - 100

x² + (10x - 10x) - 100

x² - 100

x² - 100 is your answer.

~

Answer:

x^2-100

Step-by-step explanation:

Use the F.O.I.L method

x^2+100x-100x-100

A drink is mixed in the ratio
lemonade : orange : cranberry = 6 : 3 : ?
If the fraction for cranberry juice is 3/12, what would be the missing number in the ratio?

Answers

Answer:

3

Step-by-step explanation:

 Drink mix ratio:

        Lemonade   :    Orange      :     Cranberry

                 6           :          3          :          C

  Fraction  of Cranberry juice  = [tex]\frac{3}{12}[/tex]

Sum of the ratio = 6 + 3 + C  = 9 + C

   Fraction of Cranberry;

                [tex]\frac{C}{9 + C}[/tex]   = [tex]\frac{3}{12}[/tex]

               3(9 + C)  = 12C

               27 + 3C  = 12C

               27  = 12C - 3C

                9C  = 27

                   C = 3

The missing number will be 3

Which expression is the simplest form of 5(2x - 3) - 3(x + 4) / 9

A. 7x - 3

B. 7x - 27/9

C. 7x - 3

D. 13x - 27/9 ​

Answers

Answer:

The answer is B.

Step-by-step explanation:

The simplified expression is  7x - 27/9

What is expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

Given:

5(2x - 3) - 3(x + 4) / 9

=10x-15-3x-12/9

=10x-3x-15-12/9

=7x-27/9

Learn more about expression here:

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What is the perimeter and area of a polygon?

Answers

Answer:

To find the perimeter, add together the lengths of the sides. Start at the top and work clockwise around the shape. Area of Polygon = (Area of A) + (Area of B) To find the area, divide the polygon into two separate, simpler regions.

Step-by-step explanation:

What is x if f(x)=-2

Answers

f(x) = -2

f(x) is the same thing as x

f(x) is the same thing as -2

Now think about it. If f(x) and -2 are the same thing, what is x?

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