define function. What are five representations of functions? Give an example of each.

Answers

Answer 1

Answer:

A function is a relationship between two variables, such that one variable is determined by the other variable.

A function can be represented verbally. For example, the circumference of a square is four times one of its sides.

A function can be represented algebraically. For example, 3x+6 3 x + 6 .

A function can be represented numerically.

A function can be represented graphically.

Step-by-step explanation:

Answer 2

The function is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

We need to define function.

What is a function?

Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is the set of values that have the potential of coming out as outputs of a function.

Different types of a function:

The types of functions have been classified into the following four types.

Based on the set of elementsBased on equationBased on rangeBased on domain

Representation of functions:

There are three different forms of representation of functions.

Venn Diagram: The Venn diagram is an important format for representing the function. The Venn diagrams are usually presented as two circles with arrows connecting the element in each of the circles. The domain is presented in one circle and the range values are presented in another circle. And the function defines the arrows, and how the arrows connect the different elements in the two circles.

Graphical Form: Functions are easy to understand if they are represented in the graphical form with the help of the coordinate axes. Representing the function in the graphical form helps us to understand the changing behaviour of the functions if the function is increasing or decreasing. The domain of the function - the x value is represented along the x-axis, and the range or the f(x) value of the function is plotted with respect to the y-axis.

Roster Form: Roster notation of a set is a simple mathematical representation of the set in mathematical form. The domain and range of the function are represented in flower brackets with the first element of a pair representing the domain and the second element representing the range.

Therefore, the function is defined as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

To learn more about the function visit:

https://brainly.com/question/9046022.

#SPJ2


Related Questions

need help asap please

Answers

Answer:

[tex]\displaystyle 77[/tex]

Step-by-step explanation:

Isosceles triangles will always tell you what you need to know. All angles are congruent, therefore all edges are congruent. ‍♂️

I am joyous to assist you at any time.

A band expects to put 16 songs on their next CD. The band writes and records 37.5​% more songs than they expect to put on the CD. During the editing​ process, 50​% of the songs are removed. How many songs will there be on the final​ CD?

Answers

answer:

- this is multi-step problem

16 X 1.375 = 22 songs (37.5% was added)

22 X .5 = 11 songs (50% was removed)

final answer: 11 songs.

Find the volume of the figure. Round your answer to two decimal places, if needed

Answers

Answer:

[tex]\mathrm{A. \:756\:in^3}[/tex]

Step-by-step explanation:

The volume of a rectangular prism can be represented by [tex]l\cdot w\cdot h[/tex]. The dimensions of this prism are 6x9x14.

Therefore the volume of this prism is:

[tex]6\cdot 9\cdot 14=\fbox{$\mathrm{A. \:756\:in^3}$}[/tex].

ank A contains 80 gallons of water in which 20 pounds of salt has been dissolved. Tank B contains30 gallons of water in which 5 pounds of salt has been dissolved. A brine mixture with a concentrationof 0.5 pounds of salt per gallon of water is pumped into tank A at the rate of 4 gallons per minute.The well-mixed solution is then pumped from tank A to tank B at the rate of 6 gallons per minute.The solution from tank B is also pumped through another pipe into tank A at the rate of 2 gallonsper minute, and the solution from tank B is also pumped out of the system at the rate of 4 gallons perminute. Find the differential equations with initial conditions for the amounts,x(t)andy(t), of saltin tanks A and B, respectively, at time t.

Answers

Answer:

[tex]\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}[/tex]

[tex]\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}[/tex]

x(0)=20,y(0)=5

Step-by-step explanation:

We are given that

Tank A contains water=80 gallons

x(0)=20,y(0)=5

Tank B contains water=30 gallons

Rate=4 gallon/min

Concentration of salt  is pumped into tank=0.5 pound /gallon of water

Solution pumped from tank A to tank B at the rate=6 gallons/min

Solution pumped from tank B to tank A at the rate=2gallon/min

Solution from tank B is pumped out of the system at the rate=4 gallon/min

We have to find the DE at time t

For x

Rate in=[tex]0.5\times 4+y(t)/30\times 2[/tex]

Rate in=[tex]2+y/15[/tex]

Rate out=[tex]x/80\times 6[/tex]

Rate out=3x/40[/tex]

[tex]\frac{dx}{dt}=[/tex]Rate in-Rate out

[tex]\frac{dx}{dt}=2+y/15-3x/40[/tex]

[tex]\frac{dx}{dt}=2-\frac{3}{40}x+\frac{y}{15}[/tex]

For y

Rate in=[tex]x/80\times 6[/tex]

Rate in=3/40x

Rate out=[tex]y/30\times (4+2)[/tex]

Rate out=y/5

[tex]\frac{dy}{dt}=[/tex]Rate in-Rate out

[tex]\frac{dy}{dt}=\frac{3}{40}x-\frac{y}{5}[/tex]

Please help me I will give you 10 points

Answers

Answer

Multiply 8 and 4

Step-by-step explanation:

start from left to right so you wanna start by dividing and multiplying first in evaluating

Cooper runs a farm stand that sells apples and grapes. Each pound of apples sells for $3 and each pound of grapes sells for $2.25. Cooper sold 3 times as many pounds of apples as pounds of grapes and he made $180 altogether. Graphically solve a system of equations in order to determine the number of pounds of apples sold, x,x, and the number of pounds of grapes sold, yy.

Answers

Answer:

The answer seems like it's 400 but i'm not 100% sure.

Step-by-step explanation:

How much change should Mack get back when he uses $20.00 to pay for purchases totaling $14.35?

Answers

Answer:

5

Step-by-step explanation:

i anserwed it on the test

Select the correct answer.
Which expression means five times the sum of band two?
OA. 5(6+2)
O B. 56+2
Oc. (6+2)
5
D
(5+2)
OD.

HELP PLEASE!! ill give brainlist

Answers

A is the answer to that question!

Answer:

Hi... Your answer is A...

Write the ordered pair for each given point:
9) J ___
10) E ___
11) X ___
12) Z ___
13) B ___
14) D ___
15) R ___
16) W ___

I WILL PUT BRAINLIEST!!

Answers

j:-5,9
e:-2,1
x:1,2
z:-8,-3
b:-4,-6
d:-5,1
r:-3,-8
w:0,9
j(-5,9)
e(-2,1)
x(1,2)
z(-8,-3)
b(-4,-6)
d(-5,1)
r(-3,-8)
w(0,9)

Bradley owe's his parents $275. Every week, Bradley pays his parents back $55. Which function represents the
amount of money Bradley still owes his parents?

Answers

Answer:

The function f(x) = 275-55x represents the amount of money Bradley still owes.

Step-by-step explanation:

Given that:

Amount Bradley owes = $275

Amount Bradley pays each week = $55

Let,

x be the number of weeks.

We will subtract the amount paid every weeks from the total amount, where x is the number of weeks. The function will be given by;

f(x) = 275 - 55x

Hence,

The function f(x) = 275-55x represents the amount of money Bradley still owes.


Find the slope of the line through the points (4,2) and (6,2).

Answers

Answer:

The slope is m=0

Explanation:But since the y-coordinates of the points are equal, we can find the slope easier than just by using above formula.

Explanation:But since the y-coordinates of the points are equal, we can find the slope easier than just by using above formula.If y-coordinates are equal and x-coordinates are not equal (as in our case), then the slope equals 00 (the line is horizontal).

r(x)=2square root of x S(x)= square root of x (rs)(4)=

Answers

Answer:

[tex](rs)(4) = 8[/tex]

Step-by-step explanation:

Given

[tex]r(x) = 2\sqrt{x[/tex]

[tex]s(x) = \sqrt x[/tex]

Required

Determine [tex](rs)(4)[/tex]

In functions:

[tex](fg)(x) = f(x) * g(x)[/tex]

This implies that:

[tex](rs)(x) = r(x) * s(x)[/tex]

Substitute values for r(x) and s(x)

[tex](rs)(x) = 2\sqrt{x} * \sqrt{x}[/tex]

[tex](rs)(x) = 2(\sqrt{x})^2[/tex]

[tex](rs)(x) = 2x[/tex]

Substitute 4 for x

[tex](rs)(4) = 2 * 4[/tex]

[tex](rs)(4) = 8[/tex]

A group of friends really love to go bowling together. Here are a set of final scores from a recent bowling trip:

147, 160, 80, 110, 121, 164, 62, 90, 76, 83, 110

Required:
What is the mean?

Answers

Answer:

[tex]Mean = 109.364[/tex]

Step-by-step explanation:

Given

[tex]Data: 147, 160, 80, 110, 121, 164, 62, 90, 76, 83, 110[/tex]

Required

Calculate the mean

Mean is calculated as:

[tex]Mean = \frac{\sum x}{n}[/tex]

In this case:

[tex]n = 11[/tex]

So, we have:

[tex]Mean = \frac{147+ 160+ 80+ 110+ 121+ 164+ 62+ 90+ 76+ 83+ 110}{11}[/tex]

[tex]Mean = \frac{1203}{11}[/tex]

[tex]Mean = 109.364[/tex] -- approximated

Give the coordinates of each transformation of (2, –3)
1. horizontal translation of 5
2.vertical translation of –1
3.reflection across the x-­axis
4. reflection across the y­-axis

Answers

Answer:

Step-by-step explanation:

1). The graph of y=f(x) is translated 3 units to the right. The equation that ... 2) The graph of y=g(x) is transformed by horizontally expanding it by a factor of 35 and translated 5 units to the left. ... -reflection over x- axis.

Look at the table of values.
x
у
-6
11
- 2
7
0
5
4
1
8
-3
Which equation represents the relationship between x and y?
A. y = x-1
B. y = x - 4
C. y = 5 - x
D. y = 2x + 3

Answers

C. The equation applies for each group.

Easy math (17 points))

Answers

Answer:

A-8.25  B-43.2 C-248.5

Step-by-step explanation:

Answer:

A-8.25

B-43.2

C-248.5

Step-by-step explanation:


13. Becky is playing with marbles. Of the marbles 2/3
of them are green. Among the green marbles, 1/4
of them also have polka-dots. What fraction of
Becky's marbles are green and have polka-dots?

Answers

Answer:

2/3 x 1/2 = 1/6

Step-by-step explanation:

Solve -2a - 5 > 3
Which graph shows solutions
I-Ready diagnostic

Answers

Answer:

Step-by-step explanation:

Here you go mate

Step 1

-2a-5>3  Equation/Question

Step 2

-2a-5>3  Simplify

-2a-5>3

Step 3

-2a-5>3  Divide

answer

a<-4

Hope this helps

factor polynomial
x^ + 9x + 20​

Answers

(x+4)(x+5) is the factored form

The nth term of a sequence is 2n + 1
The nth term of a different sequence is 3n - 1

Work out the three numbers that are in both sequences and also between 20 and 40

Answers

Answer:

The three numbers are 23, 29 and 35.

Step-by-step explanation:

Given: The nth term of a sequence is 2n+1 and the nth term of a different sequence is 3n-1.

To find: The three numbers that are in both sequences and also between 20 and 40.

Consider both the sequences.

Put n = 11 in the nth term 2n+1, we get 23.

So, the 11th term of first sequence is 23.

Now put n = 8 in the nth term 3n-1, we get 23.

So, the 8th term of the second sequence is 23.

Therefore, first number that is in both sequence and lies between 20 and 40 is 23.

Now put n = 14 in the nth term 2n+1, we get 29.

So, the 14th term of first sequence is 29.

Put n = 10 in the nth term 3n-1, we get 29.

So, the 10th term of the second sequence is 29.

Therefore, second number that is in both sequence and lies between 20 and 40 is 29.

If we put n = 17 in the nth term 2n+1, then we get 35.

That is, 17th term of first sequence is 35.

Now we put n = 12 in the nth term 3n-1, then we get 35.

That is, 12th term of second sequence is 35.

So, third number that is in both sequence and lies between 20 and 40 is 35.

Hence, the three numbers that are in both sequences and also between 20 and 40 are 23, 29 and 35.

Please help me! I'm really stuck on this question!

Answers

i think the answerd is a

Which mixed number is equivalent to the improper fraction?
14/9

Answers

Answer: 1 5/9 (one and five-ninths)

Given the sequence \\(\\frac{1}{4},\\frac{1}{8},\\frac{1}{16}\\)\nthen r is _____​

Answers

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

For geometric sequences, we find r by dividing one of the terms by the last. So we could do [tex]\frac{1}{\frac{16}{\frac{1}{8}}}[/tex]or [tex]\frac{1}{\frac{8}{\frac{1}{4}}}[/tex] and it'll give us the same result (1/2)

What is the answer to this Question?


8 – 6 (x – 4) = 2x – 2 (4x – 5) + 22

Answers

Answer:

Here

Step-by-step explanation:

Let's solve your equation step-by-step.

8−6(x−4)=2x−2(4x−5)+22

Step 1: Simplify both sides of the equation.

8−6(x−4)=2x−2(4x−5)+22

8+(−6)(x)+(−6)(−4)=2x+(−2)(4x)+(−2)(−5)+22(Distribute)

8+−6x+24=2x+−8x+10+22

(−6x)+(8+24)=(2x+−8x)+(10+22)(Combine Like Terms)

−6x+32=−6x+32

−6x+32=−6x+32

Step 2: Add 6x to both sides.

−6x+32+6x=−6x+32+6x

32=32

Step 3: Subtract 32 from both sides.

32−32=32−32

0=0

What ratio is bigger 6:12 or 1:2

Answers

Answer:

they are both the same amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

They are both the same 6:12  can be reduced to 1:2 by dividing 6 and 12 by 6.

Which of the following represents y as a function of x?

Answers

Answer:

The table only represent s y as function of x

Add the two expressions
-4.2x+3 and 2.5x-6


please help me with this

Answers

-1.7×-6 is the answer. Hope this helps.

Answer:

-1.7x + -3

Step-by-step explanation:

−4.2x+3 +2.5x−6

−4.2x+3

2.5x−6

Hope This Helped  <3

que porcentaje de 108 es 81?​

Answers

el porcentaje es 75%

Jina wanted to study how the area of a rectangle changes with the length if it’s width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then employed the results and connected them with a line, as shown in the picture. The graph shows the area (in m2) versus the length (in m)
Find the range and domain for the functions shown.
(A). Domain:
(B). Range:

Answers

Answer:

The domain and the range of the function are, respectively:

[tex]Dom\{f\} = [0\,m,5\,m][/tex]

[tex]Ran\{f\} = [0\,m^{2}, 10\,m^{2}][/tex]

Step-by-step explanation:

Jina represented a function by a graphic approach, where the length, measured in meters, is the domain of the function, whereas the area, measured in square meters, is its range.

[tex]Dom\{f\} = [0\,m,5\,m][/tex]

[tex]Ran\{f\} = [0\,m^{2}, 10\,m^{2}][/tex]

Answer:

Step-by-step explanation:

who knows this answer ?!!​

Answers

Answer:

D is the answer

Step-by-step explanation:

twice as many children is 24 because 12x2 is 24

Other Questions
PLEASE HELP, ill give brainliest and 10 points3. When Telemachus first encounters Odysseus, he addresses Odysseus as a stranger and a beggar. What literary device does thisdemonstrate?dramatic ironysituational ironyhyperboleverbal ironyconflict A student is investigating how substrate concentration affects the rate of anenzyme-catalyzed reaction. Which threevariables should be kept constant in the setup of thestudents investigation? Select all three variablesA. temperature of the reactionB. amount of enzymeC. amount of substrateD. amount of productE. pH of the reaction (05.05) Which of the following inequalities matches the graph? (1 point) Why are labor unions able to negotiate effectively with companies where individual workers can't?Help please 80 points!!! An element is a specific type of atom (true or false) How did Adolf Hitler take over the nation ofAustria?A. Hitler used his blitzkrieg methods.B. Hitler signed an agreement with Austria's leader.C. Hitler began the events of the Holocaust in Austria.D. Hitler bought Austria from Italy. 1Which is NOT true of homologous chromosomes? *(1 Point)they are identicalthey have genes for the same traitsthey are in pairsthey have genes that are in the same order What are the two resulting cells formedfrom a single cei cared?A Brother cellsD Parentals Find the solution of these two equations. Y=1/5x-7 and y=-x-1 Income tax returns show that the mean income of self-employed persons in a particular year was 15,000, with a standard deviation of 975. A random sample of 169 returns from people in the clothing industry gave a mean income of 14,500. Did this indicate that income from self-employment in the clothing industry was significantly different? In the figure, a square is inside another bigger square.If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is units and the length of the diagonal of the inside square rounded to the nearest tenth is units ? Can someone help ? how did trade affect the Greeks how does the royal palace in Bangkok combine the architecture of Thailand in the west we _________ sent you the installation cd in your packet. ( 1. should of 2. should have 3. shoulda 4. all of the above 5. none of the above Mindy can drive a total of 375 miles on one full tank of gas, witch is 25 gallons. based on this information, what is the constant of proportionality A 10 B. 15 C.25 D.375 What were laws passed by the states which were intended to keep African Americans down socially and economically.1. restrictive codes2. Freedmans Bureau3. slave laws4. black codes HELP ASAP Ill GIVE BRAINLIEST :))))Which of the following does - Darwins explanation for evolution was dependent on which scientific concept? The overlook on the mountain created _________________ views *10 pointsInterestingPrettyBreathtaking Isaac is making a cookie recipe that requires 3 cups of sugar for every 6 cups of flour Isaac only has 4 cups of flour he concludes that he will only need two cups of sugar A. Isaac is incorrect he needs three cups of sugar because decrease in the number of cups of flours by 2 requires increasing the number of cups of sugar by 2. B. Isaac is the correct one third of the amount of sugar is needed because only one-third of the recipe will be made. C. Isaac is incorrect the number of cups of sugar must be reduced by 2 because the number of cups of flour is reduced by 2. D. Isaac is correct he needs 2 cups of sugar because a ratio 2 to 4 is equivalent to 3to6