Find the domain and range of the following functions:
1. f(x) = 4x-3
2. G(x) = | 1-2x |
3. f(x) = x²-2x+1 / x-1

Find The Domain And Range Of The Following Functions:1. F(x) = 4x-32. G(x) = | 1-2x |3. F(x) = X-2x+1

Answers

Answer 1

The domain and range of the functions, Domain includes all possible inputs and range includes all possible outputs , are-

1. f(x) = 4x-3

Domain - all real numbers or

Range - all real numbers

2. G(x) = | 1-2x |

Domain- all real numbers

Range - All real numbers≥ 0

3. f(x) = x²-2x+1 / x-1

this can be simplified as ( x-1)²/(x-1) = x-1

Domain - all real numbers

Range- all real numbers

4. f(x) = {x-1 if x<3,

2x+1 if x ≥3 }

Domain - all real numbers

Range - All real numbers

5. y = [tex]\sqrt{4-x}[/tex]

Domain - All real numbers <4

Range - all real numbers ≥0

Mathematical functions are analogous to vending (soda) machine operations. When you put in a certain amount of money, you can choose from a variety of sodas. Similarly, when we use functions, we enter different numbers and get new numbers as a result. The primary characteristics of functions are domain and range. A soda can be purchased with quarters or one-dollar bills. If you put in pennies, the machine will not give you any soda flavor. As a result, the domain represents the inputs available here, which are quarters and one-dollar bills. A cheeseburger will not be served from a soda machine, no matter how much you pay. Thus, the range represents the possible outputs we can have here, i.e., the

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Related Questions

help me please! is compound interest

Answers

Answer:

7,200

Step-by-step explanation:

Mrs.jones waters the plants on her porch every 5 days. She waters the vegetable garden every 2 days. If she waters them both today, how many days will pass before she will water both of them on the same day again?

Answers

the answer is 10. if you take the lcm of 5 and 2 you should get it.

-9r+10r i have one more pls help me

Answers

Answer:

Step-by-step explanation:

10r - 9r = r

si en la cancha de una escuela se va a colocar 150 sillas en forma rectangular, cuales seran las posibles arreglos de manera que no sobren sillas en ninguna fila

Answers

Answer:

RGRGAEGETG

Step-by-step explanation:

which of the following is a linear function

Answers

Answer:

The 1st one?

Step-by-step explanation:

Sorry if I'm wrong

Isabella tossed a coin and spun a spinner that is divided into 3 equal sections. She did this 50 times. The results are shown in the table. What is the experimental probability that the next time Isabella tosses the coin and spins the spinner she will get a tails and a 2? *

Answers

Answer:

ur gay landen

Step-by-step explanation:

What are the real and imaginary parts of the complex number?

10−7i
The real part:

The imaginary part:

Answers

Answer:

Real: 10

Complex: -7i

Step-by-step explanation:

i is imaginary.

The real part of the complex number is 10 and the imaginary part of the complex number is -7i.

What is complex number?

The complex number is of the form a+ib where a and b are real numbers.

The given number is 10-7i.

Compare the given number with a+ib and determine the values of a and b.

a=10

b=-7

In the complex number, a+ib the real part is a and b is the imaginary part.

So, the real part of the given number is 10 and the imaginary part is -7i.

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pls help me on this

Answers

Answer:

0.3(25)

Step-by-step explanation:

Of = multiply30% = 0.330% of 25 = 0.3(25)

I hope this helps!

Translate to an equation and solve the following: h divided by −13 is equal to −65.

Answers

Answer: h=845 and equation is h/-13=-65

Steps:

h/-13=-65

Multiply both sides by -13 to eliminate fraction and isolate the h

h=845

What is the quotient of 6 -1/2

Answers

Answer:

-3

Step-by-step explanation:

because quotient means division,

so you divide 6 by -1/2

-1/2 is equal to -0.5

6/-0.5= -3

Which best describes the dimensions of a line?

A line has zero dimensions because it represents a location on the coordinate plane.
A line has one dimension because it is made up of all points that extend infinitely in either direction.
A line has two dimensions because it is made up of three noncollinear points.
A line has multiple dimensions depending on how many labeled points it contains.

Answers

Answer:

A line has one dimension because it is made up of all points that extend infinitely in either direction.

Step-by-step explanation:

The correct statement which describes the dimensions of a line is,

''A line has one dimension because it is made up of all points that extend infinitely in either direction.''

What is Line segment?

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

We have to given that;

To find the dimensions of a line.

We know that;

A line has one dimension because it is made up of all points that extend infinitely in either direction.

Thus, The correct statement which describes the dimensions of a line is,

''A line has one dimension because it is made up of all points that extend infinitely in either direction.''

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Ricky Bobby currently has $500 in his savings account, and figures that he will add $25 per week from his
job. He realizes that he can use the equation
S=25w+500 where S is the amount in savings and w= number of weeks from now.
a. How much will he have saved in 15 weeks
b. When will Ricky Bobby have $1200?

Answers

Ricky Bobby will have saved $875 in 15 weeks and he will have $1200 in 28 weeks.

Firstly solving first part of the question. Here, we need to calculate the savings in 15 weeks. To perform this calculation, we will keep the number of weeks in place of variable w.

Savings = 25×15 + 500

Performing multiplication

Savings = 375 + 500

Performing addition

Savings = $875

Now, solving the second part, which is finding the number of weeks. We will keep the savings amount at place of variable S.

1200 = 25w + 500

25w = 1200 - 500

Performing subtraction

25w = 700

w = 700 ÷ 25

Performing division

w = 28

Therefore, Ricky Bobby will have saved $875 in 15 weeks and he will have $1200 in 28 weeks.

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What is the length of JL?

Answers

As We can see that point J is on (-2,5) and L is on (-2,-2)

So we know that distance cannot be in negative, thus

Distance between J and L =5+2=7 units

JL=7

What 5 points are not coplanar with H, E, and A?

Answers

5 points that are not coplanar with H, E, and A are B, I, C, F, and G.

The figure in the given diagram is a cube. We have to find the 5 points in the cube that are not coplanar with H, E, and A.

Points are non-coplanar if they don't lie on the same plane.

From the given cube diagram, it is clear points A, E, H, J, and D lie on the same plane, while the points B, I, C, F, and G lie on a different plane. Since we have to check if the points are coplanar with respect to the given points H, E, and A.

It can be concluded that points J and D are coplanar with the given points H, E, and A as they all lie in the same plane, while the points B, I, C, F, and G are non coplanar points with respect to the given points H, E, and A as they lie on a different plane.

Therefore, using the concept of coplanar and non coplanar points, we get 5 points that are not coplanar with H, E, and A as B, I, C, F, and G.

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2 What is the solution set of
|4x - 1|= 3?

Answers

Answer:

Exact Form:

x = 1 , − 1/ 2

Decimal Form:

x = 1 , − 0.5

Step-by-step explanation:

QUICK MATH

The health benefits Daisy receives from his employer covers 45% of the total montly premium of $350.00. How much does Daisy have to pay each month?

Answers

Answer:

$192.5

Step-by-step explanation:

1. turn 45% into .45

2. multiply .45 x 350

3. get 157.5 and then subtract 350-157.5

4. answer is 192.5

7th grade what is the tone, or mood in the beginning of the play? "A christmas carol"

A- Violent and frighting
B- Dark and gloomy
C- Silly and sentimental
D- Loving and festive

Answers

Answer:

Step-by-step explanation:

C is thy answer I just took the quiz

Don’t worry about number 4 just tell me the answer to number two

Answers

Answer:

Step-by-step explanation:

First, you must combine like terms.

5a - a - a would be 3a.

-6 + 4 would be -2.

3a-2

Answer:

The answer would be B. -a+4+5a-a-6.

You would need to put like terms together. 4 and -6 is -2. -a, 5a, and -a is 3a.

In the parallelogram below, x = [? ] 6x-57 3x+3

Answers

The value of x is 20

What is a parallelogram?

A parallelogram is a quadrilateral with equal opposite sides

Since the opposite sides of a parallelogram are equal, then the following equation is true

[tex]6x - 57 = 3x + 3[/tex]

Divide through by 3

[tex]2x - 19 = x + 1[/tex]

Collect like terms, in the above equation

[tex]2x - x = 19 +1[/tex]

Evaluate the like terms

[tex]x = 20[/tex]

Hence, the value of x is 20

Answers

x=7

Pretty Simple.. h h h

The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).

What is the area of the triangle?

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

The vertices of the triangle are given as,

(x₁, y₁) ⇒ (5, 2)

(x₂, y₂) ⇒ (x, 4)

(x₃, y₃) ⇒ (0, 3)

Then the area will be

Area = 1/2[{5 × 4 + x × 3 + 0 × 2} – {2 × x + 4 × 0 + 3 × 5}]

25/2 = 1/2 [20 + 3x – 2x – 15]

25 = [x + 5]

x = 25 – 5

x = 20

The value of the variable 'x' will be 20. Then the third vertice of the triangle is (20, 4).

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Can someone tell me how to solve this? Thank you

Answers

Answer:

domain: all real numbers except x=3 and x=5.

Step-by-step explanation:

You want the domain of a composition of rational functions f(x)=1/(x-2) and g(x)=4/(x-3).

Domain

The domain of a function is the set of values of the independent variable for which the function is defined.

To compute f(g(x)), you must first compute g(x). When x=3, the denominator of the function 4/(x-3) is zero, so the value is undefined. The domain must exclude x=3.

The composition is found by substituting g(x) for x in the definition of f(x).

[tex]f(g(x)) = f(\dfrac{4}{x-3}) =\dfrac{1}{\dfrac{4}{x-3}-2}=\dfrac{x-3}{4-2(x-3)}\\\\f(g(x))=\dfrac{x-3}{4-2x+6}=\dfrac{x-3}{2(5-x)}[/tex]

We have written the composition in this form so you can see there is a denominator factor that will be zero when x=5. The domain of f(g(x)) must also exclude x=5.

The domain of f(g(x)) is all real numbers except x=3 and x=5.

PLEASE ANSWER IMMEDIATELY

Simplify the expression -416 - -613 Explain your solution using the additive inverse property.

Answers

Answer: 203

Step-by-step explanation:

-416 + 613

203

Part E
Open the parallel lines rotation application .The right set of parallel lines is a 90° rotation counterclockwise of the left set of
parallel lines. Click the 90° counterclockwise button. Are the two sets of parallel lines the same? What does this mean about
how parallel lines change when you rotate them?

Answers

Two sets of parallel lines continue to stay equidistant to each other in each set of parallel lines, this same parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.

What is Angle Translation?A translation is a type of transformation that involves sliding each point in a figure the same distance in the same direction. In geometry, translating something simply means moving it around. We do not alter it in any way. When we translate a segment, it remains a segment and its length remains constant. Similarly, when we translate an angle, the angle's measure remains constant.

According to the given diagram:

Although the two sets of parallel lines in each set remain equidistant to each other, the parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.

Therefore, two sets of parallel lines continue to stay equidistant to each other in each set of parallel lines, this same parallel line at an angle to the Y-axis will not intersect the parallel line at an angle to the x-axis if they are extended infinitely.

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WILL GIVE BRAINLIEST

The difference of two numbers is 2. Their sum is 10. Find the numbers.

Answers

Answer:

6 and 4

Step-by-step explanation:

6 + 4 = 10

6 - 4 = 2

Hope this helped you :)

6 and 4

6-4 = 2

6+4 = 10

They tell you the sum is 10, so think of #'s that make 10:

1,9

2,8

3,7

4,6

5,5

Now, which ones make 2 when subtracted

9-1 = 8

8-2 = 6

7-3 = 4

6-4 = 2

5-5 = 0

Therefore, the answers are 6 and 4

pls help I will fail 10th grade

Answers

Answer:

Step-by-step explanation:

Please mark brainiest

From 10 am to 4 pm the temperature changed -36 degrees. If the temperature changed equally for the last 6 hours, How much did it change each hour?

Answers

Answer:

-6 degrees per hour

Step-by-step explanation:

divide -36 by 6(the number of hours) and get -6

Answer:

6 degrees

Step-by-step explanation:

it changed 6 degrees every hour

Use the information to answer the question.
Consider the triangle.
16x + 5
4x + 2
8x + 1
Part A
Which expression represents the perimeter of the triangle?

Answers

Answer:

13x^8 + 4x^5 - 16x^2 try this

Step-by-step explanation:

Which line is an asymptote of the function f(x)= -6e^4(x-1) - 2 ?

A. y = 1
B. y = -2
C. y = -6
D. y = 1

Answers

Answer:

i am positive it is B

Step-by-step explanation:

it is definitely b for sure

What is the value of x in x = inverse of sin(-1/2)?

Answers

Answer:

B. -pi/6

Step-by-step explanation:

Need help ASAP!!! Please comment if you know the answer I Really need help

Answers

i’m pretty sure it’s 65% please correct me if i’m wrong :)

The answer is 65% because when you do 13/20 which will give you 0.65 which equals 65/100 which equals 65%.

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Find the domain and range of the following functions: 1. f(x) = 4x-3 2. G(x) = | 1-2x | 3. f(x) = x²-2x+1 / x-1

Answers

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Find the domain and range of the following functions:
1. f(x) = 4x-3
2. G(x) = | 1-2x |
3. f(x) = x²-2x+1 / x-1