Describe the transformations necessary to transform the graph of f(x) into that of g(x).

Describe The Transformations Necessary To Transform The Graph Of F(x) Into That Of G(x).

Answers

Answer 1

Using translation concepts, it is found that the necessary transformations are given as follows:

Reflection over the y-axis. Horizontal stretch by a factor of 2.Shift left 3 units.Reflection over the x-axis.Shift down 1 unit.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The original function f(x) is given by:

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

The transformations are as follows:

For the values of x, the function was multiplied by -1/2 and then 3 was added. Thus it was reflected over the y-axis, horizontally stretched by a factor of 2 and shifted left 3 units.Outside the domain, in the values of y, the function was multiplied by -1 and then subtracted by 1, hence it was reflected over the x-axis and shifted down one unit.

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Related Questions

What is the length of the hypotenuse of the triangle?

what is the length of the hypotenuse of the triangle?


what is the length of the hypotenuse of the triangle?


triangle a b c. side a c is 7 feet and side c b is 4 feet. hypotenuse a b is unknown.
startroot 22 endroot ft
startroot 33 endroot ft
startroot 57 endroot ft
startroot 65 endroot ft

Answers

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}[/tex]

please awnser quickly

Answers

Answer:

B': (-8,2)

C':(-8,9)

D':(-5,4)

Step-by-step explanation:

If im wrong pls tell me!



A truck's engine needs 1 gallons of oil for an oil change. How many quarts of oil are needed?

Answers

Answer:

4.8038

Step-by-step explanation:

Answer:


4


Step-by-step explanation:


there are 4 quarts  in a gallon.



hope this helps, and do you mine answering my newst quition.



Can you work out what the
next number in the pattern
should be? 4 – 6-9-6-14 - 6
-

Answers

4-6,9-6,14-6

Look the left side as right is constant (6).

9-4=514-9=5

So common difference is 5..

next no=14+5=19

Next term

19-6

Find the slope on the table

Answers

Answer:

1

Step-by-step explanation:

x = +2 you add 2 every time

y = +2 you add 2 every time

2/2 = 1

Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) -3, -23, -43, -63, ...

Answers

Answer:

1) Arithmetic since it decreases by 3 so, -3n + 38.

2) Arithmetic since it decreases by 20 each time, so -20n+17

Step-by-step explanation:

Mr. Smith works 26 hours and earns $468. If Mr. Smith works for 16 hours, how much does he earn?

I got $ 288 but I just want to make sure

Answers

Answer:

$288

Step-by-step explanation:

468 ÷ 26 = 18

so $18 per hour times 16 hours would give you $288, your right

solve fast pls i am mark you​

Answers

Answer:

[tex] \bold{ x = - \frac{5}{6} }[/tex]

Step-by-step explanation:

⠀⠀⠀⠀■ Question

[tex] \large \sf{ \frac{4x + 9}{3x + 11} = \frac{4x + 3}{3x + 2} }[/tex]

Solve for x.

⠀⠀⠀⠀□ Solution

We will cross multiply the above equation

[tex] \sf (4x + 9)(3x + 2) = (4x + 3)(3x + 11) \\ \\ \sf 4x(3x + 2) + 9(3x + 2) = 4x(3x + 11) + 3(3x + 11) \\ \\ \sf 12 {x}^{2} + 8x + 27x + 18 = 12 {x}^{2} + 44x + 9x + 33 \\ \\ \sf 12 {x}^{2} + 35x + 18 = 12 {x}^{2} + 53x + 33[/tex]

Now we will take the values of RHS(right hand side) to LHS(left hand side) of the equation. During this, the values of RHS will get opposite sign while going to LHS.

[tex] \sf 0 = 12 {x}^{2} + 53x + 33 - 12 {x}^{2} - 35x - 18 \\ \\ \sf 0 = 18x + 15[/tex]

Taking 15 to LHS

[tex] \sf - 15 = 18x[/tex]

Dividing both RHS and LHS of the equation by 18

[tex] \large{ \sf \frac{ - \cancel{15} \tiny {5}}{ \cancel {18} \tiny6 } = x} \\ \\ \boxed{ x = - \frac{5}{6} }[/tex]

Answer:

[tex]\textsf{$x=-\dfrac{5}{6}$}[/tex]

Step-by-step explanation:

Given: [tex]\textsf{$\dfrac{4x+9}{3x+11}=\dfrac{4x+3}{3x+2}$}[/tex]

1. Cross-multiply

(4x + 9)(3x + 2) = (4x + 3)(3x + 11)

2. Distribute

⟶ (4x + 9)(3x + 2) = (4x + 3)(3x + 11)

⟶ 4x(3x) + 4x(2) + 9(3x) + 9(2) = 4x(3x) + 4x(11) + 3(3x) + 3(11)

⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33

3. Combine like terms

⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33

⟶ 12x² + 35x + 18 = 12x² + 53x + 33

4. Subtract 12x² from both sides

⟶ 12x² - 12x² + 35x + 18 = 12x² - 12x² + 53x +33

⟶ 35x + 18 = 53x + 33

5. Subtract 35x from both sides

⟶ 35x - 35x + 18 = 53x - 35x + 33

⟶ 18 = 18x + 33

6. Subtract 33 from both sides

⟶ 18 = 18x + 33

⟶ 18 - 33 = 18x + 33 - 33

⟶ -15 = 18x

7. Divide both sides by 18 to isolate the variable

[tex]\longrightarrow\textsf{$\dfrac{-15}{18}=\dfrac{18x}{18}$}\\\\\\\longrightarrow\textsf{$\dfrac{-15}{18}=x$}\\\\[/tex]

8. Reduce

[tex]\longrightarrow\textsf{$\dfrac{-15\div 3}{18\div 3}=x$}\\\\\\\longrightarrow\textsf{$-\dfrac{5}{6}=x$}[/tex]

A guidance counselor reports that in a given semester, the probability that a student chooses art as an elective is 15 percent, the probability that a student chooses art or drama is 20 percent, and the probability that a student chooses both art and drama is 2 percent. what is the probability that a student chooses drama as an elective?

Answers

The probability that a student chooses drama as an elective is 7%.

What is the concept of probability?

Probability is the study of the odds of obtaining each outcome of a random experiment. These odds are assigned the real numbers in the range between 0 and 1. Results closer to 1 are more likely to occur.

In this case, we can call:

A represents ArtD represents Drama.

So, the information given was:

P(A) = 15%P(A or D) = 20%P(A and B) = 2%

The formula will be:

P(A or D) = P(A) + P(D) - P(A and D)

So:

[tex]20\% = 15\% + P(D) - 2\%\\P(D) = 20\% - 15\% + 2\%\\P(D) = 7\%[/tex]

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SOMEONE HELP ME PLEASEE

Answers

Answer:

area: 165yd^2 perimeter:26yd or 33yd

Step-by-step explanation:

11ydx15yd= 165yd^2

11yd+15yd=26yd

Answer:

56.1, 36.2

Step-by-step explanation:

For this we need to use the Pythagorean Theorem, which is a^2+b^2=c^2. We have our a and c values, so we can make the equation 11^2+b^2=15^2, or 121+b^2=225. Next, we isolate b.

121+b^2=225

-121         -121

___         ___

0             104

b^2=104

Now, we have to find the square roots of both sides. If we do this, we get b= 10.2.

Now, we can find our perimeter:

11+15+10.2= 36.2

For area, the formula is 1/2(b)h (1/2 times the base and height), so:

1/210.2=5.1

5.1*11=56.1

Hope this helps!

what is t - s

please help me

Answers

t - s

-7-(-4)

-7+4

-3

hope it helps...!!!

Answer:

Top Secret

Step-by-step explanation:

top secret. Slang. tough sh#t (a euphemistic initialism used to avoid explicit vulgarity). See also sh#t (def. 31).

Not what you're looking for?

During a sale the regular price of an item is reduced by 20 percent if the sale price is $600 what is the regular price

Answers

The regular price is $750

What is the solution to the equation



m - 8 = 12

Answers

Answer:

m= 20

Step-by-step explanation:

add 8 to both sides,

12+8=20

NEED HELP QUICK - State the reference angle and what quadrant the terminal side of the angle is in.

Answers

Answer:

the answer is 225

Step-by-step explanation:

y+135=360

y=360-135

y=225

I will give BRAINILEST

Answers

Answer:50%

Step-by-step explanation: there is no real answer to your question because 50%is not there

Write each decimal as a fraction in simplest terms

Answers

Answer:

A. 25/33

B. 1/3

C. 1/33

D. 25/9

Answer:

Step-by-step explanation:

11. Find the equation for the circle with center ​(−2​,−3​) and passing through ​(1​,5​).

Answers

Answer:

(x +2)² + (y+3)² = 73

Use the distance formula to find radius:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

where (x1, y1), (x2, y1) are points

[tex]\rightarrow \sf \sqrt{(-2-1)^2+(-3-5)^2}[/tex]

[tex]\rightarrow \sf \sqrt{73}[/tex]

Eqaution of circle:

(x-h)² + (y-k)² = r²

(x-(-2))² + (y-(-3))² = (√73)²

(x +2)² + (y+3)² = 73

The neighborhood movie store rents a game machine for $12.50 plus $1.50 per day. the downtown store rents the same machine for $4 per day with no initial fee. after how many days will the total rental charge be the same for each store?

Answers

In 5 days the total rental charge is the same for each store.

What is an 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.

Given that:-

A movie store rents a game machine for $12.50 plus $1.50 per day. The downtown store rents the same machine for $4 per day with no initial fee.

Let x be the days. The two-equation will be formed as:-

Total amount = 1.5x   +   12.5  

Total amount = 4x

For the same total amount, we will equate the two equations.

1.5x   +   12.5  =  4x

12.5  =  4x  -  1.5x

12.5  =  2.5x

x  =  12.5  /  2.5

x  =  5 days

Therefore In 5 days, the total rental charge is the same for each store.

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RIGHT triangular prisms A and B are congruent. What is the volume of prism B? A) 420 in3 B) 1080 in3 C) 2160 in3 D) 32400 in3

Answers

Answer: B

Step-by-step explanation:

Which statements are true regarding this scenario? check all that apply. the sample space is {1, 2, 3, 4, 5, 6}. the expected value for the game is 0. the expected value for the game is one-half. the game is fair because the expected value is equal to 0. the game is unfair because the expected value does not equal 0.

Answers

Based on the game involving rolling a number cube, the applicable statements are:

The sample space is {1, 2, 3, 4, 5, 6}. The expected value for the game is 0. The game is fair because the expected value is equal to 0.

What happens in a game involving rolling a number cube?

There are six sides of a number cube which means that the sample space is all the sides the cube can land on which are 1,2,3,4,5, and 6.

Because there are 3 odd numbers which can give you a negative point, and 3 even numbers which can give a point, the expected value is 0 as these cancel each other out.

This makes the game fair because situations that have an expected value of 0 are considered fair because there are no expected losses or profits.

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Answer:

A,C,D

Step-by-step explanation:

short and simple for you ;)

D = {x:x is an integer -3

Answers

Answer:

yes , because -3 is the whole number

Ms. lewis has 20 students in her p.e. class.
she puts each student's name in a hat and will select
the names of 2 students at random as team leaders for
a volleyball game. how many different pairs of team
leaders could she choose?

Answers

Considering the definition of combination, she could choose 190 different pairs of team.

What is combination

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following formula is applied:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Different pairs of team leaders

Ms. lewis has 20 students in her p.e. class. She puts each student's name in a hat and will select the names of 2 students at random as team leaders for a volleyball game.

So, you know that:

m= 20n= 2

Replacing in the definition of combination:

[tex]C=\frac{20!}{2!(20-2)!}[/tex]

Solving:

[tex]C=\frac{20!}{2!18!}[/tex]

C= 190

Finally, she could choose 190 different pairs of team.

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please please please help me this is for my brother.​

Answers

Answer:

below

Step-by-step explanation:

it was the first thing I saw

Plssss helllpp. Worth 10 points
What is a synonym for the word "partial?"

incomplete
one-sided
complete
different

Answers

Answer:

incomplete

or

The first one

Step-by-step explanation:

hope this helps

have a good day

The area of the garden is 13.92 square meters. A fence is planned around the perimeter of the garden. How many meters of fencing are needed?

Answers

The meters of fencing that is needed is = 3.36m

Calculation of needed meters

The garden is designed in a trapezoid form with sides= a; 3.3m and b; 5.28m.

The area of the trapezoid garden = 13.92 m²

Therefore the meters of fencing needed which is height = ?

The formula for the area of trapezoid = A = (a+b/2)h

From the formula make h the subject of formula;

h = A *2/a+b

h = 13.92*2/3.3+5.28

h =27.84/8.28

h= 3.36m

Therefore, the meters of fencing that is needed is = 3.36m.

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how to do this please help me​

Answers

Answer: ∠BAC = 70°

Step-by-step explanation:

    We will use the "Exterior Angle Property" which states that an exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

   This means that (6a) + (7a) = 130° which we can solve.

(6a) + (7a) = 130°

13a = 130

a = 10°

    Now that we have the value of a, we can solve for the angle BAC.

7a

7(10)

70°

can someone help me please I'm exhausted can someone find the quotient of 36.8 divided by 2.3

Answers

Answer:

16

Step-by-step explanation:

36.8÷2.3=16 with no remainders

Answer:

16

Step-by-step explanation:

36.8 divided by 2.3 is 16

12. Select all the numbers that are greater than 1.
a.
23
b.
0.63
7
C.
1
-
5
5
d.
7
N
2
e.
w
Im
2.
f.

Answers

Answer:

its 23, (0.63 maybe), 7 ,5,5 that’s it

Step-by-step explanation:

7.
Quadrilateral PQRS is inscribed in a
circle. The ratio of m/P to m/R is 2: 4.
What is mZR?
F 30°
H 120°
G 60°
Not here

Answers

Answer: Ha

Step-by-step explanation:

5. Graph the hyperbola ya
16
What are the equations of the asymptotes?

Answers

Answer: y = ± [tex]\frac{4}{3}x[/tex]

Step-by-step explanation:

Just believe it, it's the right one. I don't know how to explain it.

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