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.

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Related Questions

Solve 3[-x + (2 x + 1)] = x - 1.
x = 2

Answers

Answer:

x = -2

Step-by-step explanation:

[tex]3[- x + (2x + 1)] = x - 1[/tex]

[tex] = > 3[ - x + 2x + 1 ] = x - 1[/tex]

[tex] = > 3[x + 1] = x - 1[/tex]

[tex] = > 3x + 3 = x - 1[/tex]

[tex] = > 3x - x = - 1 - 3[/tex]

[tex] = > 2x = - 4[/tex]

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

PLEASE HELP ITS EASY IM JUST TERRIBLE AT MATH!!!! ILL MARK BRAINLIEST. How many 1/8 are in 1 and 1/4
WRITE YOUR ANSWER AS A FRACTION NOT A MIXED NUMBER!!
PUt correct answer too please

Answers

There are 8 1/8 in 1 and 2 1/8 in 1/4

Hope this helps ^W^

Answer:

There are 8 - 1/8's in 1; andThere are 2 - 1/8's in 1/4.

Uncle John has 32 lemon trees and 28 lime trees to plant on his grove. He would like to plant the trees in rows where each row has the same number of lemon trees and each row has the same number of lime trees. What is the greatest number of rows Uncle John can plant?

Answers

Answer:

The greatest number of rows is 10.

To find this you can do 32 plus 28 which equals 60 then you know 60 divided by 10 is 6 so you could have six rows and six columns or 10 rows and six columns and 10 is greater than six.

So, the greatest number of rows you can have is 10.

Solve the system by substitution.
-9x – 2y = -44
8x – 3 = y

Answers

Answer:

x = 2, y = 13

(2, 13)

Step-by-step explanation:

hope this helps!

9/20 = ?/100
I need help please

Answers

Answer:

45

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

Which of the following is a solution to the system of two equations y = 3x – 7 and 4x – 5y = -20?

Answers

Answer:

x = 5, and y = 8

Step-by-step explanation:

You can solve this system by solving either of the equations for either x or y, and substituting that into the other.

Since the first equation is already defined for y, let's substitute that into the second equation:

4x - 5y = -20

4x - 5(3x - 7) = -20

4x - 15x + 35 = -20

4x - 15x = -20 - 35

-11x = -55

x = 5

We can then plug that into either of the original equations to find y:

y = 3x - 7

y = 3 * 5 - 7

y = 15 - 7

y = 8

We can also verify our answer by plugging one of the values into either of the original equations and seeing what we get:

4x - 5y = -20

4x - 5 * 8 = -20

4x - 40 = -20

4x = 20

x = 5

So we know the answer is correct.  x is equal to five, and y is equal to eight.

??????????????????????

Answers

Answer:

f(8)=91 is the answer

answer is 91

NOT GRADED.
FIND THE MEASURE OF THE INDICATED ANGLE IN EACH TRIANGLE.​

Answers

Answer:

The angle in the box is always 50 and that other acute angle is 46

Hope this helps

Step-by-step explanation:

Answer:

m∠B = 44°

Step-by-step explanation:

∑ of all angles in a triangle = 180°.

Note that m∠C = 90° (based on the definition of a right angle).

Note that m∠A = 46° (given).

Set the equation:

Total (180) = 90 + 46 + m∠B

Isolate the term, m∠B. First, simplify. Combine like terms:

180 = (90 + 46) + m∠B

m∠B + (136) = 180

Next, note the equal sign, what you do to one side, you do to the other. Subtract 136 from both sides:

m∠B + 136 (-136) = 180 (-136)

m∠B = 180 - 136

m∠B = 44°

44° is the measurement of the indicated angle B.

~

Zane has 30 cupcakes and wants to give six each to a number of his friends.How many friends can he do this for ? ​

Answers

5 friends this one was pretty easy
The answer is 5 because if you do the math 30 divided by 6 it equals 5

help pls due today thanks

Answers

Answer:

18/3 is 6

-18/3 is -6

-18/(-3) is 6

18/(-3) is -6

X^2+ 2x – 35 = 0? .............

Answers

There are two possibilities for the above question

If u have read the book Ungifted by Gordon Korman then hopefully u can answer this question: Consider the two schools in the book; the Academy for Scholastic
Distinction and Hardcastle Middle School. In what ways are they
similar or different? Consider the physical space, school cultures,
lunchroom offerings, and students.

Answers

Answer:

similar

Step-by-step explanation:

A dripping faucet leaks 40 gallons of water per day.

How many gallons does the faucet leak in 2 days.

Answers

Answer:

80 gallons and a leaking problem.

Step-by-step explanation:

please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!

(lol optional): add my sc: tealyn337

DO U LIKE MATHEMATICS QUESTIONS

Answers

Answer:

No lol

Step-by-step explanation:

I actually hate maths..

I do not but I have to do them if I want to pass math

Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30% are shipped to the people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other people, but for only 10% of the orders shipped to the person making the order.

a. What is the probability that a randomly selected order will be a gift wrapped and sent to a person other than the person making the order?
b. What is the probability that a randomly selected order will be gift wrapped?
c. Is gift wrapping independent of the destination of the gifts? Justify your response statistically?

Answers

Answer:

0.18 ; 0.1875 ; No

Step-by-step explanation:

Let:

Person making the order = P

Other person = O

Gift wrapping = w

P(p) = 0.7 ; P(O) = 0.3 ; p(w|O) = 0.60 ; P(w|P) = 0.10

What is the probability that a randomly selected order will be a gift wrapped and sent to a person other than the person making the order?

Using the relation :

P(W|O) = P(WnO) / P(O)

P(WnO) = P(W|O) * P(O)

P(WnO) = 0.60 * 0.3 = 0.18

b. What is the probability that a randomly selected order will be gift wrapped?

P(W) = P(W|O) * P(O) + P(W|P) * P(P)

P(W) = (0.60 * 0.3) + (0.1 * 0.7)

P(W) = 0.18 + 0.07

P(W) = 0.1875

c. Is gift wrapping independent of the destination of the gifts? Justify your response statistically

No.

For independent events the occurrence of A does not impact the occurrence if the other.

Are the following triangles similar to each other? If so, why?

Answers

Yes the are simailer because of SSS

Calculate the average rate of change of function on the interval (a,a+h). simplify your expression.Show all steps.
f(x)=3x+2/2x-1

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=\frac{3x+2}{2x-1}[/tex]

at x₁ = a,

[tex]f\left(x_1\right)=f\left(a\right)=\frac{3a+2}{2a-1}[/tex]

at x₂ = a+h,

[tex]f\left(x_2\right)=f\left(a+h\right)=\frac{3\left(a+h\right)+2}{2\left(a+h\right)-1}[/tex]

Using the formula to determine the average rate of change

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                      [tex]=\:\frac{\frac{3\left(a+h\right)+2}{2\left(a+h\right)-1}-\frac{3a+2}{2a-1}}{a+h-a}\:\:\:\:\:\:\:[/tex]

as a+h-a = h, so    

                      [tex]=\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

Thus, the everarge rate of chnage:  [tex]\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

We can further simplify such as:

[tex]=\frac{\frac{3\left(h+a\right)+2}{2\left(h+a\right)-1}-\frac{3a+2}{2a-1}}{h}[/tex]

[tex]=\frac{-\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}}{h}[/tex]

[tex]=-\frac{\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}}{h}[/tex]

[tex]=-\frac{7h}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)h}[/tex]

Cancel the common factor h

[tex]=-\frac{7}{\left(2a-1\right)\left(2\left(h+a\right)-1\right)}[/tex]            

A travel agent calculates the cost of a trip to Paris using this formula C = p(t + 30).

C is the total cost in pounds

p is the number of people

t is the cost of the trip per person

Use this formula to calculate the total cost if p = 2 and t = 245.

Answers

Answer:

C=550 pounds

Step-by-step explanation:

Given the formula: C=p(t+30)

and with p=2 and t=245 known.

We can plug our values of p and t into our formula. Once we do this, the only unsolved variable will be C.

C=2(245+30)

Add 245+30 first because they are in parentheses and we must abide by the order of operations.

C=2(275)

Now we just multiply 2(275) because this is all that's left in the formula.

C= 2*275 = 550

We now know that C=550 when p=2 and t=245, but we need to apply units to finalize the answer. We are told that C represents the total cost in "POUNDS", so pounds is our units for variable C.

Our final answer is...

C=550 pounds

I need help with this word problem please

Answers

Answer:

Step-by-step explanation:

Given function is,

f(x) = [tex]x\sqrt{x}[/tex]

We can rewrite this function as,

f(x) = [tex]x^{\frac{3}{2}}[/tex]

a). Domain of the function is [0, ∞)

Derivative of the function in this domain,

f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]

     = [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]

Since, f'(x) > 0 in the interval [0, ∞)

Function is increasing in the interval [0, ∞)

b). For local maxima and local minima,

  Second derivative of the function,

  f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]

         = [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex]  > 0

   So the function should have a local minima.

   But the function is continuous in the interval x ≥ 0,

   There is no local minima (only absolute minima).

c). Since, second derivative is undefined at x = 0,

   There are no inflection points.

d). Since, f"(x) > 0 in the interval [0, ∞)

   Concavity of the curve is UPWARDS.

Rewrite the following equation as a function of x
1/16x + 1/320y - 29 = 0
A. F(x) = -9280 + 1/16x
B. F(x) = 9280 - 20x
C. F(x) = -9280 + 20x
D. F(x) = 9280 - 1/16x

Answers

Answer:

the awnser is b hope this helps

Step-by-step explanation:

The equation as a function of x is f(x)=9280-20x. Therefore, option B is the correct answer.

The given function is x/16 + y/320 - 29 = 0.

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.

Now, the LCM of denominators 16 and 320 is 320.

So, 20x/320 + y/320 - 9,280/320 = 0

⇒20x+y-9280=0

⇒y=9280-20x

The equation as a function of x is f(x)=9280-20x. Therefore, option B is the correct answer.

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3x − 2y = 18
y = 2x − 13

Answers

Answer:

x = - 8

3x - 2y = 18 is the same as 3x - (2x - 13 times 2) = 18

Then I used an algebra site for the rest.

It should be x = - 8

I'm guessing you want x and y solved.

Answer: x=10 and y=6

Explanation:

For X: Substitute the y-equation (y-2x-13) into the first equation (3x-2y=18) so your equation is 3x-2(2x-13)=18. Do the distribution property and the equation will be 3x-4x+26=18. Put like terms on the same side of the equal sign and combine like terms (subtract 26 on both sides) and the equation will be -x = -10. To make x positive, make both sides positive and you get x=10.

For Y: Substitute your x answer (10) into the first equation (3x-2y=18) and you will get 30-2y=18. Subtract 30 from both sides and you get -2y=12. Divide both sides by the common factor of -2 and you get y=6.

Please answer correctly i will give brainliest

Answers

Answer: It is C

Step-by-step explanation:

Good luck on your test or homework

what is the domain of the function on the graph?

Answers

Answer:

c

Step-by-step explanation: because

plwase answer ALL the blanks.

Answers

Answer:

its option A

Step-by-step explanation:

ben sells greeting cards for $5 each in his online store. He also charges $1.99 for shipping. The total cost, y, of an order from Bens store is found using the equation y = 5x+ 1.99, where x is the number of cards bought. Which quantity represents the dependent variable in this problem situation?

Answers

Answer: How many greeting cards he sells

Step-by-step explanation:

The cards are 5 dollars each. 1.99 for shipping is all the same. The only thing that changes is the amount that he sells. So the amount of Greeting cards sold is the dependent variable.

A 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.

15.69 feet
18.01 feet
27.89 feet
36.72 feet

Answers

Answer:

hope this helps, brainlist? (OwO)

Step-by-step explanation:

I think the answer is 27.89 feet, C

The building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Lenght of the ladder = 32 foot

The angle formed between the ladder and the ground = 29.37°

The ladder, wall of the building, and the ground are making a right-angle triangle.

Let's suppose the base of the ladder is x feet far from the building.

Applying the Cos ratio to find the value of x:

[tex]\rm Cos29.37\°=\frac{x}{32}[/tex]

x = 27.887 feet or     (Cos29.37°  = 0.871)

x = 27.89 feet

Thus, the building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.

Know more about trigonometry here:

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Janie and Jasmine are playing three games at an arcade. Each of the games requires either 2, 3, or 4 tokens. The girls plan to play as many games as they can before running out of tokens. Let m represent the number of games that require 2 tokens; n represent the number of games that require 3 tokens; and p represents the number of games that require 4 tokens.

Janie plays the 3-token game four times. Write two equivalent expressions to represent the number of tokens that Janie will need to play each of the three games at least one time.​

Answers

12

3 + 3 + 3 + 3 = 12

3 x 4 = 12

Thanks!! <3

Find the measure of each angle in the problem: complementary angles with measures 4x and 5x-18 degrees

Answers

Answer:

42 degrees and 48 degrees

Step-by-step explanation:

If they are complementary, that means they add up to 90 degrees, so

4x + 5x - 18 = 90,

Solving,

9x - 18 = 90

add 18 to both sides

9x = 108

divide both sides by 9

x = 12

Now, to find the angle measures of each you have to substitute x = 12 into both angles.

4x --> 4 * 12 = 48 degrees

5x - 18 --> 5 * 12 - 18 --> 60 - 18 --> 42 degrees

Daniela buy records for 9$ each she buys 8 records how much money does Daniela spend

Answers

Answer:

FGCG

Step-by-step explanation:

Answer:   72 dollars

Step-by-step explanation:

each=1

1 record cost 9$

8 record costs (9)(8)$

I did multiplication here

(9)(8)=72 $

PLEASE HELP Which statement completes step 5 of the proof?


Step 1 segment KL is parallel to the y-axis, and segment JL is parallel to the x-axis.

Step 2 ΔJKL was rotated 90° clockwise to create ΔJ'KL'. Point K did not change position, so it remains point K. Therefore, ΔJKL ≅ ΔJ'KL'.

Step 3 segment K L prime is perpendicular to the y-axis, and segment J prime L prime is perpendicular to the x-axis.

Step 4 segment JK lies on line f and has a slope of 3.

Step 5 ?

Step 6 The product of the slopes of segment JK and segment J prime K is −1; therefore, lines f and g are perpendicular.

Answers

Answer:

Segment J’K lies on line g and has a slope of -1/3

Step-by-step explanation:

Im taking the test but I need step 4 but step 5 is filled in for me

Answer:

In case you get the same question

Step-by-step explanation:

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