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

Solve for m.
m+9=-2

m=?

Answers

11
subtract 9 to both sides

Answer:

-11

Step-by-step explanation:

Because you just carry the nine over which when you switch it sides it becomes negative so it's -9 + -2 which equals negative 11

2.8 x 10^3=

What is the answer

Answers

Answer:

9.24

Step-by-step explanation:

2800 take it or leave it

1. How can you tell the difference between the pre-image and image when only given the coordinates or a picture.

Answers

Step-by-step explanation:

if u pour all the liquid in a cone into a cylinder with the same height and radius then you will fill half of the cylinder with liquid

Answers

Answer:

No, the liquid will not fill half of the cylinder

Step-by-step explanation:

The volume of a cylinder is 3 times bigger than a cone with equal radius and height

To know this we have to compare the volumes of both solids first.

Let us assume the height and radius of the cone and radius are

6 and 2 mm respectively

so that the volume of a cone is given as

Volume of cone= 1/3 πr^2h

and the volume of cylinder is given as

Volume of cylinder= πr^2h  

1. Volume of cone= 1/3 πr^2h

Volume of cone= 1/3 *3.142*(2)^2(6)

Volume of cone= 75.408/3

2.  Volume of cylinder= πr^2h

Volume of cone= 3.142*(2)^2(6)

Volume of cone= 75.408

From the analysis the volume of a cylinder is three times bigger the volume of a cone with similar radius and height

Fertilizer for your lawn has to be mixed with water. Every 5 ounces of mix needs 1 gallon of water. How many cups of mix do you need if you are using 8 gallons of water?

Answers

Answer:

  5 cups

Step-by-step explanation:

There are 8 ounces in a cup, so the ratio given is ...

  5/8 cup : 1 gallon

Multiplying this by 8, we have ...

  5 cups : 8 gallons

If you are using 8 gallons of water, you need 5 cups of mix.

im sorry I got the answer wrong and and was trying to delete it my original answer was 40 before zI realized i said ounces

Triangle EFG has vertices E(–3, 4), F(–5, –1), and G(1, 1). The triangle is translated so that the coordinates of the image are E’(–1, 0), F’(–3, –5), and G’(3, –3).

Which rule was used to translate the image?

T4, –4(x, y)
T–4, –4(x, y)
T2, –4(x, y)
T–2, –4(x, y)

Answers

Answer:

C.) T2, -4(x, y)

Step-by-step explanation:

did on edge :)

The rule of translation of the triangle EFG is (c) T-2,4(x,y)

How to determine the translation rule?

We  have:

Pre-image: E(–3, 4), F(–5, –1), and G(1, 1).Image: E’(–1, 0), F’(–3, –5), and G’(3, –3).

Taking E and E', we have:

E = (-3, 4)

E' = (-1, 0)

Subtract E from E'.

So, we have:

(x, y) = (-1 + 3, 0 - 4)

Evaluate

(x, y) = (2, -4)

This can be rewritten as:

T-2,4(x,y)

Hence, the rule of translation is (c) T-2,4(x,y)

Read more about translation at:

https://brainly.com/question/4289712

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Given h(x) = 3x + 4, solve for x when h(x) = 1
(Will mark brainliest)

Answers

Answer:

x is -1

Step-by-step explanation:

subtract 4 from 1 to get -3, then you have -3+3x then divide both sides by 3 to get x+-1

Answer:

-1

Step-by-step explanation:

1. nine more than thirty divided by ten

Answers

Answer:

3.9

Step-by-step explanation:

nine more than thirty=39

39/10=3.9

Look carefully at the graph and find the slope.

Answers

Answer:

1/10

Step-by-step explananation:

-2(x + 4) + 5x = 4

It's easier than it looks, but I still have problems.

Answers

[tex] \huge\boxed{Answer:} [/tex]

[tex] \sf -2(x + 4) + 5x = 4 \\\\\sf

=-2x-8+5x=4 \\\\\sf

=5x-2x-8-4=0 \\\\\sf

=3x-12=0 \\\\\sf

=3x=12 \\\\\sf

x=\frac{12}{3}\\\\\sf

x=\frac{ \cancel{12}}{ \cancel{3}}\\\\\sf

x=4

[/tex]

Hi, I am from India......

Happy to help you..

Which is a rational number?
-15/4
-7/9
4 with a rational sign?
pi

Answers

Answer:

All are rational numbers I guess

Step-by-step explanation:

NoTE : I'm not sure

Answer:

For the first one its 7/9 ig

Find the value of the variable.

Answers

Answer:

boom ganag

Step-by-step explanation:

Jesse wants to purchase three binders and a backpack. If the backpack costs $16, which equation represents the situation in which x denotes the cost per binder and y denotes the total cost of Jesse’s purchase?

Answers

16+3x=y
The 16 is the cost of the backpack, which you add to the 3 binders which cost x each. This gives you the total, y.

Hope this is helpful!!

The equation represents the situation in which x denotes the cost per binder and y denotes the total cost of Jesse’s purchase is 16+3x=y.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jesse wants to purchase three binders and a backpack. If the backpack costs $16

From the data given in the question:

The linear equation can be framed as follows:

y = 16 + 3x

Or

16 + 3x = y

Thus, the equation represents the situation in which x denotes the cost per binder and y denotes the total cost of Jesse’s purchase is 16+3x=y.

The options are:

16+y=3x

16+3x=y

y+3x=16

3+16x=y

Learn more about the linear equation here:

brainly.com/question/11897796

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A recycling center has 100 kilograms of shredded plastic yogurt containers. What volume in m3 is needed to hold this amount of shredded plastic? Assume the lowest density within the range.

Answers

AnswerI dont kow

Step-by-step explanation:

What is the y intercept of this graph?. What is the slope?

Answers

Answer:

y intercept is -3

slope is 4

y=4x-3

Step-by-step explanation:

someone please help me

Answers

Answer:

1/49 it is the equal to that

Step-by-step explanation:

I

what is the unit rate of (0,0) and (12, 16)
A) 0.25 cm/s
B) 0.33 cm/s
C) 0.75 cm/s
D) 1.33 cm/s

Answers

To integers between eight is six and seven

To integers between eight is six and seven c

Which is the right answer?

Answers

Answer:

Most likely B.

Step-by-step explanation:

A. When being compared to each other, they're not alternate interior angles.

B. I think so...?

C. Angle 3 is the only interior angle.

D. Pretty sure that they have to be on the same line to count as "supplementary".  

The domain for the graph (in interval notation) is

Answers

Answer:

Domain: [-3, 1]

Step-by-step explanation:

Doman is the set of x-values that can be inputted into function f(x).

We see that our x-values span from -3 to 1. Since both have no holes, they are included in our domain:

[-3, 1] or -3 ≤ x ≤ 1

Omari and his two cousins received the same amount of money to go to the movies. Each boy spent $15. Afterward, the boys had $30.75 altogether. How much money did each boy receive?

Answers

Answer:

Each boy recieved $25.25 each

Step-by-step explanation:

First, you add up all the money the 3 boys spent.

15+15+15=45

Then you add the sum of the equation to the amount all the boys had afterward.

45+30.75=75.75

Finally, you divide that product to 3 boys.

75.75/3=25.25

Therfore the answer is $25.25 each.      

2.5/6 = h/9 h=? What does this mean

Answers

Answer:

h = 3.75

Step-by-step explanation:

Step 1: Write equation

2.5/6 = h/9

Step 2: Solve for h

Cross multiply: 22.5 = 6hDivide both sides by 6: 3.75 = hRewrite: h = 3.75

Step 3: Check

Plug in h to verify it's a solution.

2.5/6 = 3.75/9

0.416667 = 0.416667

Answer:

h = 3.75

Step-by-step explanation:

Given

[tex]\frac{2.5}{6}[/tex] = [tex]\frac{h}{9}[/tex] ( to solve for h, cross- multiply )

6h = 22.5 ( divide both sides by 6 )

h = 3.75

Greg has a container of building blocks that has 4 blocks in each row and 8 blocks in each column. How many
blocks are in Greg's container?

Answers

Answer:

If we are doing mulibleing

Step-by-step explanation:

8 x 4 is 32.

8 divided by 4 is 2.

What would the answers be for 2. And 3.?

Answers

Answer:

H and B

Step-by-step explanation:

For number 3 its B because pie = irrational

Answer:

For number 2 the answer is J.

For number 3 the answer is B.

Step-by-step explanation:

2. f(x)=2x+10

f(-8)=2(-8)+10

f(-8)=(-16)+10

f(-8)= -6

3. Pi is an irrational number so 32 with pi will also be irrational.

-2.5(-2-3x)+2.5(-4x-1)=-2x-4x

Answers

Answer:

x=−0.714286

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−2.5(−2−3x)+2.5(−4x−1)=−2x−4x

(−2.5)(−2)+(−2.5)(−3x)+(2.5)(−4x)+(2.5)(−1)=−2x+−4x(Distribute)

(7.5x+−10x)+(5+−2.5)=(−2x+−4x)(Combine Like Terms)

Step 2: Add 6x to both sides.

Step 3: Subtract 2.5 from both sides.

Step 4: Divide both sides by 3.5.

x=−0.714286

Which unique point on this graph can represent the slope of the graph and the unit rate of change in the snow level?​

Answers

Answer:I will give you an answer ,but I can't unless I can see the graph

Step-by-step explanation:

How do you isolate a variable?

Answers

Answer:

a variable is isolated by using the many properties.

these are addition, subtraction, division, and multiplication

Step-by-step explanation:

hope this helps!

2. Solve 8(4-x) = 10

Answers

[tex] x = 2 \frac{3}{4} [/tex]

Step-by-step explanation:

[tex]8(4 - x) = 10[/tex]

Expand :

8(4-x) = 32-8x

[tex]32 - 8x = 10[/tex]

Collect like terms and simplify

[tex] - 8x = 10 - 32 \\ - 8x = - 22[/tex]

Divide through by -8

[tex] \frac{ - 8x}{ - 8} = \frac{ - 22}{ - 8} [/tex]

Simplify

[tex]x = 2 \frac{6}{8} \\ \\ x = 2 \frac{3}{4} [/tex]

Answer:

x=2.75. 8(4-2.75)=8(1.25)=10.

P.s.

Please give me brainliest.

What is 3/2
5= Pls help me i have no clue and i have a math test soon pls help me

Answers

Answer:

15/2

Step-by-step explanation:

You have 3/2 5so you do 3 x 5 which is 15 then you have the answer. You keep the bottom number the same always

Solve for a.

a+0.3=−2

Answers

Answer:

a = −2.3

Step-by-step explanation:

Move all terms not containing  a  to the right side of the equation.

Answer:

a = -2.3

Step-by-step explanation:

move 0.3 onto the other side so it becomes -0.3now it is : a = -2 - 0.3(-2 - 0.3) is just -2.3a = -2.3

Purpose is important because it reminds you why you're doing what you're doing when things get tough
O True
O False

Answers

the answer the this question is TRUE because without purpose why are you doing what you’re doing?
True, when times are tough and everything looks like it’s going the wrong way then the thought of a Purpose will help push someone to move forward in order to fill their purpose.
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