The exponential function f(x) = 2x undergoes two transformations to
g(x) = 1/3• 2x – 7. How does the graph change? Select all that apply.
A. It is shifted right.
B. It is shifted down.
C. It is flipped over the x-axis.
D. It is vertically compressed.
E. It is vertically stretched.

The Exponential Function F(x) = 2x Undergoes Two Transformations Tog(x) = 1/3 2x 7. How Does The Graph

Answers

Answer 1

Answer:

Shifting down.

Vertically compressed

Step-by-step explanation:

Given

[tex]f(x) = 2^x[/tex]

[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]

Required

Determine the translation from f(x) to g(x)

The first translation from f(x) towards g(x) is:

[tex]f(x) = 2^x[/tex]

[tex]f'(x) = 2^x - 7[/tex]

This is derived by:

[tex]f'(x) = f(x) - b[/tex]

Where

[tex]b = 7[/tex]

Notice that, in the above, b (i.e. 7) was subtracted from f(x), this implies that the function shifted down

The next translation that resulted in g(x) is:

[tex]g(x) = \frac{1}{3}(2^x - 7)[/tex]

This is derived by:

[tex]g(x) = a.f'(x)[/tex]

By comparison:

[tex]a = \frac{1}{3}[/tex]

Since the value of a is less than 1, then f'(x) is vertically compressed to give g(x).

Hence, the transformations that apply from f(x) to g(x) are:

Shifting down. Vertically compressed

Answer 2

Answer:

shifting down

vertically compressed

Step-by-step explanation:


Related Questions

Which is true about the functional relationship shown in the graph?
A. The shipping cost is a function of the weight of the package.
B. The weight of the package is a function of the number of packages.
C. The shipping cost is a function of the number of packages.
D. The weight of the package is a function of the shipping cost​

Answers

Answer:

A. The shipping cost is a function of the weight of the package.

Step-by-step explanation:

the input value x and the output value y, and  y is a function of x

Answer:

j

Step-by-step explanation:

What Does an E at the End of a Number Mean?
in a calculator

Answers

Answer:

Exponent

Step-by-step explanation:

Answer:

exponent

Step-by-step explanation:

What is 65 percent of 30,000?

Answers

Answer:

19500

Step-by-step explanation:

A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor informs patients of a new medication and asks if they want to participate; 30 patients who are currently taking medication for cholesterol volunteer to be part of the study. She uses random assignment of the 30 patients to two treatment groups: one that uses the new medication, and one that uses the original medication. Which of the following describes the benefit of random assignment?

The variability between the medications would be evenly distributed between the two groups, so any observed differences in the cholesterol level between the two groups would more likely be due to the subjects.
The variability between the medications would be evenly distributed between the two groups, so any observed differences in the cholesterol level between the two groups would be guaranteed to be due to the subjects.
The variability between the subjects would be evenly distributed between the two groups, so any observed differences in the cholesterol level between the two groups would more likely be due to the new medication.
The variability between the subjects would be evenly distributed between the two groups, so any observed differences in the cholesterol level between the two groups would be guaranteed to be due to the new medication.

Answers

Answer:

The variability between the subjects would be evenly distributed between the two groups, so any observed differences in the cholesterol level between the two groups would more likely be due to the new medication.

Step-by-step explanation:

Edge 2020/2021

Answer:

c

Step-by-step explanation:

edge

Y= 1/3x-1
Y=-3x-1
Y=3x-1
Y=1/3x+1

Answers

Answer:

y=3x-1

Step-by-step explanation:

Right triangle EFG and right triangle EHG overlap as shown below. Angle HEG measures 35° and angle FGE measures 30°.



What are the values of x and y?

Answers

Answer:

x=25°

y=25°

Step-by-step explanation:

E^+F+EG^F=180°(sum of int. angles of triangle)

x+35+90+30=180

x=180-90-30-35

×=25

HE^G+H+G=180° (sum of int. angles of triangle)

35+30+y+90=180

y=180-90-35-30

y=25

5)
Write the following in function notation.
y = 3x - 10
A)
x = 3y - 10
B)
f(x) = 3y - 10
C)
f(x) = 3x - 10
D)
f(y) = 3x - 10

Answers

Answer:

C

Step-by-step explanation:

What is 2(-9x-4y-7) simplified

Answers

-18x-8y-14 because you need to distribute the digits

The ratio of orange juice concentrate to water that Zoe used to make orange juice yesterday was 3 : 7. She used 14 ounces of water in the juice yesterday. Today she wants to make twice as much orange juice. Is the relationship between the amount of orange juice concentrate c and the amount of water a proportional? Explain.

Answers

Answer:

14

Step-by-step explanation:

please help me with this ​

Answers

Answer: x^2 + y^2 = 36

When an item worth more than 15,000 is given to someone, what is this tax called?

sales

gift

estate

present​

Answers

Answer:

B. Gift

Step-by-step explanation:

Taxation can be defined as the involuntary or compulsory fees levied on individuals or business entities by the government to generate revenues used for funding public institutions and activities.

A gift tax can be defined as a type of tax that is imposed or levied on property or money that is being transferred (given) as a gift from one person to another. Thus, in this type of scenario, there are no financial incentives or compensation for this items being gifted.

Basically, the annual gift tax exemption or exclusion for this year is $15,000 per recipient.

Hence, when an item worth more than 15,000 is given to someone, this tax is called gift tax.

A MOVIE THEATRE HAS TWO ROOMS. ROOM A HAS 9 ROWS WITH 18 SEATS IN EACH ROW. ROW B HAS THREE TIMES AS MANY SEATS AS ROOM A. HOW MANY SEATS ARE THERE IS BOTH ROOMS?

Answers

pretty sure it’s 162

HELP PLZ.
will give brainliest

Answers

Answer:

D

Step-by-step explanation:

The cost to join a yoga studio is 100$, plus 25$ per month. What is the cost of the first 8 months at the yoga studio?

Answers

I believe it is 275$ but not certain

Or maybe me and you as 2 yeah

On a hike, Twyla traveled from an altitude of 527 meters to an altitude of 487 meters. Which statement uses absolute value correctly? *

Answers

Answer:

Difference, D = 40

Step-by-step explanation:

This question requires options. Since there's none, I'll answer generally.

Represent the distances with d1 and d2

d1 = 527 Meters

d2 = 487 Meters

Required

Determine the absolute difference

The absolute difference (D) of the given distances can be calculated using the following expression

D = |d1 - d2|

Substitute values for d1 and d2

D = |527−487|

D =|40|

D = 40

Hence, Twyla traveled 40 meters.

need the answer now pls

Answers

Answer:

35x-35y

Step by step explanation: I

0.5(20x-50y+36)-0.25(100x+40y-12)

10x-25y+18+25x-10y+3 -------- after we distribute 0.5&-0.25

10x+25x-25y-10y+18+3. ---------we collect the like terms to add them or substract

35x-35y+21 -----------------------------simplified form

Answer:

35x-35y

Step-by-step explanation:

simply simplify both sides then subtract

Anyone can help me out with this please

Answers

Answer:

the first one, the fourth one, and the last/fifth one

Step-by-step explanation:

I believe that you were technically supposed to put the variables and numbers in, but it's easier if you just use Desmos :)

Answer:

a d e

Step-by-step explanation:

everything In red is correct

HELP ASAP PLEASE
What is the equation of the line tangent to the function f(x) = 1 – x2 at x = –3?
y = 6x + 10
y = 6x + 26
y = –6x – 8
y = –6x – 26

Answers

Plug the formula into Desmos and even just visually

C.  " y = -6x - 8

is the answer

The equation of the line tangent to the function f(x) = 1 – x² at x = –3 will be y = –6x – 8. Option C is correct.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the function is,f(x) = 1 – x²

We have to find the equation of the line tangent to the function f(x) = 1 – x² at x = –3.

Determine the function's first derivative f(x), To get the slope at a given location, plug the specified point's x value into f'(x). To determine the tangent point's y coordinate, plug the value of x into f(x). The point-slope formula may be used to combine the slope from step 2 with the point from step 3 to produce the equation for the tangent line.

Thus, the equation of the line tangent to the function f(x) = 1 – x² at x = –3 will be y = –6x – 8.Option C is correct.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

what is 1/4 of 7/2...................................

Answers

Answer:

0.875 or 7/8

Step-by-step explanation:

1/4

because it is lesser

if it was greater then

it would be 7/2

4;
Mark wants to fence 4 rectangular gardens, each with a length of4 feet and a width of 2 feet. What is the total length of fencing Mark needs to
surround all 4 gardens?
Mark needs
feet of fencing.

Answers

Answer:

48 ft

Step-by-step explanation:

perimeter of rectangular garden=2(l+b)

=2(4+2) = 12ft

for such 4 gardens = 12×4

=48ft of fencing needed

Answer:

length of rectangular garden =4feet

width =2feet

perimeter of rectangular garden=2(l+b)

=2(4+2)

=2*6

=12

total fencing needs for 4 rectangular gardens=

=12*4= 48feet

Step-by-step explanation:

hope my answer is helpful to you

Choose the best graph that represents the linear equation: 3y + 9x = 21

a. Graph A
b. Graph B
c. Graph C
d. Graph D​

Answers

Answer:

c. Graph C

I hope this helps!

Solve the inequality –1 > –2(x – 4) – 5(4x – 7).

Answers

Answer:

[tex]x > 2[/tex]

Step-by-step explanation:

[tex]–1 > –2(x – 4) – 5(4x – 7)[/tex]

[tex]–1 > –2x + 8 –20x + 35[/tex]

[tex]–1 > - 22x + 43[/tex]

[tex] - 1 - 43 > - 22x[/tex]

[tex] - 44 > - 22x[/tex]

[tex] \frac{ - 44}{ - 22} < \frac{ - 22x}{ - 22} [/tex]

[tex]2 < x[/tex]

[tex]x > 2[/tex]

Slope 8 ​; through ​(4​,3​)

Answers

Answer:

y=8x-29

Step-by-step explanation:

Since we know the slope (m) is 8, we can plug it in the slope-intercept formula y=mx+b, making y=8x+b.

Now we need to find the y-intercept (b). To do that, you would need to plug in the points given to you, which were (4,3).

x=4, y=3... so 3=8(4)+b

Now you can solve for the variable b to find the y-intercept.

3=8(4)+b, multiply...

3=32+b, subtract 32 on both sides...

-29=b

Therefore, the y-intercept, or b, is -29.

The equation would be y=8x-29

Can someone tell me the answer to me pls I have to be done in 20 minutes ​

Answers

Answer:

x = 9.25

Step-by-step explanation:

It is given that ABC is an isosceles triangle.

m∠A = 43° and m∠C = (6x+13)°

We need to find the value of x.

The sum of a triangle is equal to 180°.

∠A is the vertex angle. For a triangle sum of angle of triangle is equal to 180°

∠A+∠B +∠C=180

43+∠B+(6x+13)°=180

6x+∠B+56=180

6x+∠B = 124

∠B =124-6x

For an isosceles triangle,

∠B = ∠C

124-6x = (6x+13)

124-13 = 6x+6x

111 = 12x

x = 9.25

So, the value of x is 9.25.

What is the determinant of the coefficient matrix of the system?
please help!!!

Answers

Answer:

Third option: 0

Step-by-step explanation:

edge2020

Answer:

The answer is 0!

Step-by-step explanation:

edge 2021

whats 5.267 X N = 526.7

Answers

Answer:

N=100

Step-by step explanation

Count how many times the decimal gets moved to the right in this case it moved to the hundredths place therefore the answer is 100

Part 2: PLEASE HELP!!

Answers

Answer:

Nonlinear function

Step-by-step explanation:

It is visual that the graphed function is not linear

................................

Nonlinear function

..................................

Redondea ala décima: 0.985​

Answers

Answer:

0.990

Step-by-step explanation:

The ratio of Val's savings to Dan is 2:3 at first. After Dan spent P3000.00, Val's saving became 11/3 more of that Dan's remaining savings. What is the total amount of saving the two had at first

Answers

Answer:

P.7500.00

Step-by-step explanation:

We are told that:

The ratio of Val's savings to Dan is 2:3 at first.

Now, Dan spent P3000.00 and Val's saving became 1⅓ more of that Dan's remaining savings.

Let's say the total amount of savings they had at first was x.

Thus;

Val had: 2x/5

Dan had: 3x/5

Now, Dan spent P3000.00.

So amount Dan has left = (3x/5) - 3000

We are told Val's savings is now 1⅓ = 4/3 times that of Dan's remaining savings

Thus; 2x/5 = (4/3)((3x/5) - 3000)

2x/5 = 12x/15 - 4000

Multiply through by 15 to get;

6x = 12x - (3000 × 15)

6x = 12x - 45000

Rearranging, we have;

12x - 6x = 45000

6x = 45000

x = 45000/6

x = P.7500

The total amount of saving the two had at first is P7500 and this can be determined by using the arithmetic operations and given data.

Given :

The ratio of Val's savings to Dan is 2:3 at first.After Dan spent P3000.00, Val's saving became 4/3 more of that Dan's remaining savings.

Given that the ratio of Val's savings to Dan is 2:3 at first. Now, assume that the total amount of savings they had at first was x. So:

Val's had - 2x/5

Dan's had - 3x/5

Now, it is also given that Dan's spent P3000. So, the amount left is:

[tex]\rm =\dfrac{2x}{5}-3000[/tex]

It is given that Val's saving became 4/3 more of that Dan's remaining savings. That is:

[tex]\dfrac{2x}{5} = \dfrac{4}{3} \times\left( \dfrac{3x}{5}-3000 \right)[/tex]

[tex]\dfrac{6x}{20} = \dfrac{3x}{5}-6000[/tex]

[tex]x = \dfrac{45000}{6}[/tex]

x = P.7500

The total amount of saving the two had at first is P7500.

For more information, refer to the link given below:

https://brainly.com/question/13101306

Round 27,141 to the nearest ten

Answers

27, 140 is the correct answer
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