Which of the following statements is true of the function ? Question 2 options: A) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x right by 3 units and downward by 5 units. B) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units. C) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x right by 3 units and downward by 5 units. D) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 5 units and downward by 3 units.

Which Of The Following Statements Is True Of The Function ? Question 2 Options: A) G(x) Can Be Graphed

Answers

Answer 1

Transformations are operators that can act on functions, modifying them in different ways. In this particular problem, we see the translations.

The correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x)=  1∕x left by 3 units and downward by 5 units.

Let's describe the transformations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the shift is to the left.

If N is negative, the shift is to the right

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

Now that we know this, let's see the problem.

We have:

[tex]g(x) = \frac{1}{x + 3} - 5[/tex]

So, the original function is:

[tex]f(x) = \frac{1}{x}[/tex]

Now from f(x) we can apply translations to create g(x).

If first, we apply a translation of 3 units to the left, we get:

[tex]g(x) = f(x + 3) = \frac{1}{x + 3}[/tex]

If now we apply a translation of 5 units downwards, we get:

[tex]g(x) = f(x + 3) - 5 = \frac{1}{x + 3} - 5[/tex]

So we can conclude that the correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units.

If you want to learn more about translations, you can read:

https://brainly.com/question/12463306


Related Questions

the polygons in each pair are similar. Find the missing side length​

Answers

Answer:

Since they are similar, 45/27=30/18=x/24. x=40

Julie has 5.00 and wants to buy some glue at Walmart glue cost 4.25 how much will julie get back in change and you have to subtract a d slove problem

Answers

Answer:

read below vv

Step-by-step explanation:

d = 5.00 - 4.25

d = 0.75

Answer:

Julie will get back 0.75 in change.

Step-by-step explanation:

d=4.25

5.00-d => 5.00-4.25 = 0.75

Hope this answered your question!

subtract the following polynomial (4x+7)-(x+1)

Answers

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]\sf{(4x+7)-(x+1) }[/tex]

[tex]\sf{4x+7-x-1 }[/tex]

[tex]\sf{4x-x+7-1 }[/tex]

[tex]\sf{3x+6 }[/tex]

Given the function f(x)= (x+3)^2 determine the value of f^-1 (49) include a complete solution

Answers

Answer:

Step-by-step explanation:

taking the inverse is essentially saying

x = (f(x) + 3)^2

root(x) - 3 = f(x) and -root(x) -3 = f(x)

(you have to take both the positive and negative roots)

plug in 49 for x and get 4 and -10.

The value of the inverse function, to the function f(x) = (x + 3)², at f(x) = 49, is; f⁻¹(49) = 4

What does the inverse notation f⁻¹(x) represents?

The notation f⁻¹(x) represents the inverse of the function f(x). The inverse function, f⁻¹(x) undoes the the effect of the function f(x), meaning, that if y = f(x), then x = f⁻¹(y)

The value of f⁻¹(49) for the function, f(x) = (x + 3)² is the x-value, such that f(x) = 49, which can be obtained by solving the equation f(x) = (x + 3)², for x as follows;

Taking the square root of both sides of the equation, we get;

√(f(x)) = √((x + 3)²)

√(f(x)) = (x + 3)

Subtracting 3 from both sides, we get;

√(f(x)) - 3 = x + 3 - 3 = x

√(f(x)) - 3 = x

The above function is the inverse function, f⁻¹(x) that takes an output value, f(x), to produce the corresponding input value, x of the original function;

The inverse function, f⁻¹(x) = √(f(x)) - 3, takes the original output, f(x) to produce the original input x

When the output value is f(x) = 49 we get;

f⁻¹(49) = √(49) - 3 = ±7 - 3

Restricting the domain of the original function, f(x) to (x + 3) ≥ 0, or x ≥ -3, so that its inverse is also a function and produces only one value, we get;

f⁻¹(49) = 7 - 3 = 4

f⁻¹(49) = 4

Learn more on the inverse of a function here: https://brainly.com/question/1559611

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Write the set of non-negative integers in the inequality 2x < 4.

Answers

Answer:

The set [tex]S[/tex] of non-negative integers in the inequality [tex]2x < 4[/tex] is

[tex]S = \{0, 1\}[/tex]

Step-by-step explanation:

The non-negative integers are given as [tex]\mathbb{Z}_{\ge 0} = \{ 0, 1, 2, \ldots \}[/tex]

For the inequality [tex]2x < 4[/tex], we have

[tex]2x < 4 \implies x < \dfrac{4}{2} \implies x < 2[/tex]

Therefore,

[tex]x\in \mathbb{R}:x\in(\infty, 2)[/tex]

Note: 2 is not included

The integers are

[tex]\ldots -2, -1, 0, 1[/tex]

And the non-negative integers are

[tex]0, 1[/tex]

5x
If f(x) = 5x and g(x)= 5x/3, find f(x) divided by g(x).

A. 1/3

B. 3

C. 3/25x^2

D. 25x^2/3

Answers

i think its b Step-by-step explanation:

[tex] \frac{5x}{ \frac{5x}{3} } = \frac{15x}{5x} = 3[/tex]

Find the mean of first 5 prime numbers.

Answers

Answer:

5.6

Step-by-step explanation:

First five prime numbers:

[tex]2,3,5,7,11[/tex]

Add them up:

[tex]2+3+5+7+11=28[/tex]

Calculate the mean:

[tex]\frac{28}{5} =5.6[/tex]

Answer:

8.5

Step-by-step explanation:

We need to find the mean of first five prime numbers . We know that the first five prime numbers are ,

[tex]\sf\longrightarrow First \ 5 \ Prime\ numbers \ = 2, 3, 5 ,7,11 [/tex]

We know that mean is ,

[tex]\sf\longrightarrow Mean =\dfrac{Sum \ of \ observations}{Number\ of\ observations } [/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow Mean =\dfrac{ 2+3+5+7}{2}[/tex]

Add the numbers in numerator ,

[tex]\sf\longrightarrow Mean =\dfrac{ 17}{2} [/tex]

Divide ,

[tex]\sf\longrightarrow\boxed{\blue{\sf Mean = 8.5 }} [/tex]

Hence the mean is 8.5

pls help me both questions
with explanation sum

Answers

9514 1404 393

Answer:

  3) x = 55, y = 123, z = 123

  4) x = 276°

Step-by-step explanation:

3)

Angles P and Q are alternate interior angles, so are congruent.

  P = Q

  3x -42° = 2x +13°

  x = 55° . . . . . . . . . . . add 42°-2x

Then Q = 2x +13 = 2(55°) +13° = 123°.

Angles Y, P, Q, and Z are all congruent, so all have the same measure.

  Y = Z = 123°

__

4)

If you draw a horizontal line parallel to AB and CD through point O, then small angle POQ is divided into parts that are congruent with angles APO and CQO. That is, small angle POQ = 48° +36° = 84°.

Large angle POQ is then 360° -84° = 276°

could you tell me how
to do pls​

Answers

Answer:

f) 60+x+30=180°

90+x=180°

x=180-90

x=90°

g) y+35+75=180°

y+110=180

y=180-110

y=70°

please help !!!



12. JKL = ONM by SAS. Select one set of corresponding parts that could be marked congruent by CPCTC.

Answers

Answer:

D

Step-by-step explanation:

The statement of congruency shows which vertices are corresponding.

Answer: D  

[tex]\sqrt{2} \frac{7}{8}[/tex]

Answers

Answer:

[tex]\sqrt{2\frac{7}{8} } =\\\sqrt{\frac{25}{8} } =\\\sqrt{\frac{25*2}{16} } =[/tex]

±5√2/4

Let E= {prime numbers less than 30} Work out n(E)

Answers

Answer:

10

Step-by-step explanation:

E={2,3,5,7, 11, 13, 17, 19, 23, 29}

therefore,

n(E)={10}

Answer:

10 if I recall correctly

ugh ,, im stuck again :( someone please explain this !!!

Answers

Answer:

63cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the two triangles

Area of the rectangle = 6(3+14)

Area of the rectangle = 6 * 17

Area of the rectangle = 102cm²

Area of the smaller triangle = 1/2 * 3 * 6

Area of the smaller triangle = 18/2 = 9cm²

Area of the larger triangle = 1/2 * 6 * (17-7)

Area of the larger triangle = 1/2 * 6 * 10

Area of the larger triangle = 60/2 = 30cm²

Area of the shaded part = 102 - (9+30)

Area of the shaded part = 102 - 39

Area of the shaded part = 63cm²


Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression
that can be used to determine the final cost of the DVD. HELP URGENTLY PLEASE

Answers

Answer:

If u add the number it will show u te answer which is 7

Step-by-step explanation:

3 9. There are 180 girls in a mixed school. the ratio of girls to boys is 4:3 find the otal number of students in the school (a) 25 students (b) 315 students (c) 360 students 405 students of the binary numbers:​

Answers

The ratio 4:3 means for every 4 girls there are 3 boys.

Divide total girls by 4, multiply that by 3 to get total boys:

180/4 = 45 x 3 = 135

There are 135 boys

For total students add boys and girls:

180 + 135 = 315 total students

Instructions: Point T is the centroid. Find TE if XE= 21.

Answers

Answer:

TE = 7

Step-by-step explanation:

The centroid divides a median in this ratios 1/3 and 2/3. In particular

XT = 2/3 XE

XT = 2/3 * 21

XT = 14

TE = 7

Enda has job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The other company offers a starting salary of $55,000 with a raise of $5,000 each year. In how many years would Brenda's salary be the same with both companies? What will the salary be?

Answers

Answer:

8 years

Salary: $95000

Step-by-step explanation:

Write an equation to model the salary and its raise per year. Add the base salary to the raise per year salary times (x). Where the parameter (x) represents the number of years spent in the company.

Company (1):

75000 + 2500x

Company (2):

55000 + 5000(x)

One is asked at which year will the salaries be the same. Equate the two expressions and solve for the variable (x):

75000 + 2500x = 55000 + 5000(x)

Inverse operations:

75000 + 2500x = 55000 + 5000x

20000 + 2500x = 5000x

20000 = 2500x

8 = x

Substitute (x) into any one of the experssions and simplify to solve the epxression,

55000 + 5000(x)

x = 8

= 55000 + 5000(8)

= 55000 + 40000

= 95000

!!!!!!URGENT!!!!!
Two similar rectangles have a proportional coefficient of 1:2, and the perimeter of the smallest one is 80 m, find the
perimeter of the small rectangle

Answers

Answer:

160m

Step-by-step explanation:

Since the rectangles are similar and we have their proportion of coefficient, the larger rectangle is twice the smaller rectangle.

Furthermore, the ratio of two longer sides should equal the ratio of the two shorter sides.

Therefore, for our case, we multiply the smaller rectangle by 2.

Hence;

(80 × 2)m

= 160 m

NB:

The ratio of the areas of two similar shapes or figures is equivalent to the square of the corresponding sides.

a handbag was purchased for Rs.280/- and sold for Rs.350/- calculate profit%

Answers

Answer:

profit is 25%

Step-by-step explanation:

profit%=sp-cp/cp×100%

=350-280/280×100%

=0.25×100

=25%

Help I don’t understand this

Answers

In this you’re just finding the values of the function for the given x values.

f(0) is the y value when x=0, so you look at the graph at x=0 and look at what y value is at the point. At x=0 you get y=1, so f(0)=1.

Same thing with the other function. g(-8)= -6.

Then you substitute those values.

-8(1) + 4(-6) = -8-24 = -32

Add-ons Helplast edit was seconds ago
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E A monthly service fee to download ebooks is $4.96 plus $3.99 per book downloaded White an
equation that represents the total cost, c, in a month when books are downloaded Explain how
yos gation represents the greem
Graph
Create a graph for

Answers

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CA Geometry A Illuminate Credit 4 FF.pdf
all 4 pls

Answers

Answer:

1) HL=LJ=63

(ZJ)²=16²+63²

(ZJ)²=256+3969

ZJ=√4425

ZJ= 65

2)HJ=HL+LJ

= 63+63

HJ=126

3) XC=XA=8

4) BE=AB/2=20/2=10

OAmalOHopeO

what is the volume if the radius is 7m and the height is 9m.​

Answers

63 is the answer because 7x9=53

Una empresa textil dedicada a la confección y venta de pantis Glamour realiza la siguiente promoción de sus productos: para pedidos de hasta una decena, el par de pantis Glamour de cualquier tamaño lo vende a S/. 5. Pero si se hacen pedidos mayores a una decena de pares, cada par de media tiene un valor de S/. 3.

Answers

Respuesta:

S / 25

S / 45

S / 75

Explicación paso a paso:

Dado :

Para pedidos de hasta una docena; par de pantimedias Glamour Costo S / 5

Para pedidos de más de una docena; par de pantimedias Glamour Costo S / 3

Función de costo:

Para x ≤ 12

Costo, C = 5x

Para x> 12

Costo, C = 3x

Costo de 5 pedidos:

x = 5

Costo, C = 5 (5) = S / 25

Costo de 15 pedidos:

x = 15

Costo, C = 3 (15) = S / 45

Costo de 25 pedidos:

x = 25

Costo, C = 3 (25) = S / 75

.
A football is punted from a height of 2.75 ft above the ground, with an initial velocity of 48 feet per
second. The motion of the football can be modeled by the equation h = -16t2 + 48t +2.75, where
h represents the height of the football, in feet, and t represents the timelin seconds.
If the football is caught 5.25 ft above the ground, approximately how long did it remain in the air?
Roundyour answer to the nearest hundredth of a second.

Answers

Answer:

Step-by-step explanation:

The position function for this is given as

[tex]h(t)=-16t^2+48t+2.75[/tex] where h(t) is the height of the football at any time t. If the ball is caught at 5.25 feet, that h(t) value is 5.25 since we are looking for the time the ball was in the air from its initial 2.75 feet to 5.25 feet, when it was caught.

[tex]5.25=-16t^2+48t+2.75[/tex] and set this equal to 0:

[tex]-16t^2+48t-2.5=0[/tex] and factor.

When we factor we get

t = .05 and t = 2.95 in seconds.

That first time tell us how long it takes to go from the initial height of 2.75 to a point 2.5 feet higher, 5.25. To get get back down to the 5.25 foot height on the other side of the vertex, is 2.95 seconds. So the total time the ball was in the air was 3 seconds exactly.

Which of the following statements must be true based on the diagram below?
(Diagram is not to scale.)

Answers

Answer:

i dont know

Step-by-step explanation:

i dont kow

Pam and Amanda and Mike work at different clothing stores. Amanda made twice what Pam earned and Julie
made $90 more than Amanda. If their total earnings for a week are $995, how much did each person make?

Answers

Answer:

Pam: $181

Amanda: $362

Julie: $452

Step-by-step explanation:

(What does Mike have to do with this problem?)

Let a = Amanda's pay

Let p = Pam's pay

Let j = Julie's pay

"Amanda made twice what Pam earned"

a = 2p

"Julie made $90 more than Amanda"

j = a + 90

j = 2p + 90

Pam earned p

Total salary

a + p + j = 2p + p + 2p + 90

Total salary

$995

2p + p + 2p + 90 = 995

5p = 905

p = 181

a = 2p = 2(181) = 362

j = 2p + 90 = 362 + 90 = 452

Answer:

Pam: $181

Amanda: $362

Julie: $452

If f of x equals the quotient of the quantity x squared minus 36 and the quantity x plus 6 is continuous at x = -6, find f(-6).

Answers

Answer:

f(-6) = -12

Step-by-step explanation:

If you immediately plug in x=-6 and solve it (x^2-36)/x+6, you will not get the right answer.

You need to first expand the perfect square on the numerator (x^2-36) into (x-6)(x+6).

With the perfect square expanded, notice how you have the term (x+6) on both the numerator and denominator. You can cancel out both terms, and you will be left with (x-6).

Now you can plug in x=-6, which will give you -12.

The measure of two complementary angles are 2x degree and 3x degree, then value of x is​

Answers

Answer:

2x+3x=90

or ,5x=90

or,x=90/5

X=18

Answer:

90/5=18 degrees

Step-by-step explanation:

What are the values of x and y? A) X= 9/2; y = 9 B) x = 1843 ; y= 983 C) x= 9; y = 983 OD) x= 913 ; y=9​

Answers

Answer:

Y = 9

Cause the Sin30 = 0.5

and 9² + x² = 18²

324 - 81 = x²

x² = 243

x = 9 √3

The answer becomes "D"

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