Mathematics High School


consider the function f(x)=6sin(x-pi/8)+8. What transformation results in g(x)=6sin(x-7pi/16)+1?​

Answers

Answer 1

Answer: we have a vertical shift of 7 units down, and a horizontal shift of 5*pi/16 units to the right.

Step-by-step explanation:

First, let's define the transformations:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Here we have:

f(x) = 6*sin(x - pi/8) + 8

and the transformed function:

g(x) = 6*sin(x - (7/16)*pi) + 1

We can assume that the transformations are a vertical shift of A units, and an horizontal shift of B units, then we can write:

g(x) = f(x + B) + A

g(x) = 6*sin(x + B - pi/8) + (8 + A) = 6*sin(x - (7/16)*pi) + 1

Then we must have that:

(x + B - pi/8) = x -  (7/16)*pi

B - pi/8 = -(7/16)*pi

B = -(7/16)*pi + pi/8 =  -(7/16)*pi +2*pi/16 = (-7 + 2)*pi/16 = -5*pi/16

And we also must have that:

8 + A  = 1

A = 1 - 8 = -7

Then the transformation is:

g(x) = f(x - 5*pi/16) - 7

This means that we have a vertical shift of 7 units down, and a horizontal shift of 5*pi/16 units to the right.

Related Questions

a car traveled 360 miles in 9 hours, what is the average rate of the car miles per hour?

Answers

Avg speed = total distance /total time

360/9 = 40

The avg rate of the car is 40 mph

Yo i just copped these for my bird. How they look?

no bully pls ;c

Answers

Answer:

they look good lol

Step-by-step explanation:

Can someone help me with this, I don't understand.​

Answers

3rd one is the answer

If you put 3 to the x, then the y is 5
Also another ones too

It’s a Pythagoras question.
Given that a = 5.6 and b = 7.1 work out the perimeter of the triangle.
Give your answer rounded to 1dp

Answers

Answer:

22

Step-by-step explanation:

c²= a²+b²= (5.6)²+ (7,1)²=9

P=5.6+7.1+9=21,7=22

What is the x intercept of the line below?

Answers

Answer:

i think it is -5

Step-by-step explanation:

-5

Answer:

there is no x-intercept

Explanation:

the line does not cross the x-axis at any point. hoped this helped.

i need help with this question...
2x + 3 ≤ 13

Answers

Answer: x ≤ 5

Step-by-step explanation:

x is greater than or equal to 5. you can subtract 3 from each side of the inequality, and then divide by 2. you then have the answer.

Find the answer in simplest form.
3 1/8 * 1 4/5=

Answers

Answer:

31/8*14/5=10*17/20

Step-by-step explanation:

Answer:

225/40 which can simplify to 5 and 5/8

Step-by-step explanation: 3 and 1/8 turns into 25/8, 1 and 4/5 turns into 9/5. Multiply numerator by numerator then denominator by denominator to get 225/40, which simplifies out to 5 and 5/8.

3. A number written in scientific notation is a product of two factors.
One of the factors is a power of 10. Describe the other factor.

Answers

Answer:

You can find the product of a number and a power

of 10 by moving the decimal point of the number.

– If the exponent is positive, move the decimal point to

the right.

– If the exponent is negative, move the decimal point to

the left.

• You may need to write zeros to the right or left of

the number in order to move the decimal point.

Step-by-step explanation:

anyone know how to do this help

Answers

Answer:

Height if the tree: 13.8 meters

Answer:

Height of the tree: 13.8 meters

It took Jude 420 seconds to walk home from school. How many minutes did it take him?

9 minutes
6 minutes
7 minutes
5 minutes

Answers

Answer:

7 minutes

Step-by-step explanation:

420/60 = 7 minutes

Answer:

7

Step-by-step explanation:

420/60 which equals 7 mim

10 Sami asked 60 people which sports they liked from rugby, football and cricket. 8 people like all three sports. 17 people like rugby and football. 13 people like football and cricket. 19 people like rugby and cricket. 35 people like football. 27 people like cricket 30 people like rugby. a) How many people liked neither rugby or football or cricket?

Answers

Answer:

9 people liked neither rugby or football or cricket.

Pls tell me where to put what in the picture below

Answers

Answer:

M is the gradient of the line and b is the y-intercept or where the line cuts the y-axis and the x is zero at the point

Step-by-step explanation:

Anybody know the answer to these

Answers

M= -3
K=-5
X=3.1
There are the first 3 answers

The monthly fees for the local pool are $8 per month
and $2 per visit. If Hector pays $34 in pool fees total for
the month, how many times did he visit the pool?

Answers

Given:

Monthly fees for the local pool are $8 per month  and $2 per visit.

Hector pays $34 in pool fees total for  the month.

To find:

The number of times he visit the pool.

Solution:

We have,

Monthly fee of pool = $8

Additional fee = $2 per visit

Let Hector visit x times.

Additional fee for x times = $2x

Total fee = Monthly fee + Additional fee

[tex]34=8+2x[/tex]

[tex]34-8=2x[/tex]

[tex]26=2x[/tex]

Divide both sides by 2.

[tex]\dfrac{26}{2}=x[/tex]

[tex]13=x[/tex]

Therefore, Hector visit the pool 13 times.

If the pattern in the table continues when will sales for DVD players equal sales for mobile phones?
answer choices
never
year 2011
year 2010
year 2012

Answers

Answer:

never because they are continually increasing at the same rate without multiplying and dividing

1/x-2 +5/x / 5/x - 1/x-2

Answers

The android is 75 divided between two of the 5

Mrs. Barnes washed 2 7 of her laundry. Her son washed 1 4 of it. Who washed most of the laundry? How much of the laundry still needs to be washed? Solve this on paper. Then check your work on Zearn. Who washed most of the laundry?

Answers

Answer:

first u gotta take a step then kidnap a kid from brazil and then solve the problem

Step-by-step explanation:

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Her son washed the most laundry.

The number of laundries that need to be washed is 46.5%.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

The number of laundries Mr. Barnes washed = 2/7.

This means,

= 2/7 x 100

= 28.5%

The number of laundries her son washed = 1/4.

This means,

= 1/4 x 100

= 25%

We see that,

Her son washed the most laundry.

The number of laundry needs to be washed.

= 100% - (28.5% + 25%)

= 100% - 53.5%

= 46.5%

Thus,

Her son washed the most laundry.

The number of laundries that need to be washed is 46.5%.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ5

What value of m would make the expression below simplified to 6x

Answers

I thinks it’s A because I did this before

Someone i need help the question is 50 points.


Just answer it no explanation.

Answers

Answer:

okay buddyn

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

HELP!! Shelley creates a logo using two similar icicle triangle shown below what is the length of side s in centimeters

Answers

Answer:

s = 12cm

Step-by-step explanation:

Since these are similar triangles, in order to find a missing side, you have to find the constant of proportionality

14/8 = 21/s          >> cross multiply

14s = 168             >> divide both sides by 14 to get s alone

s = 12

another way to find the answer......

Step-by-step explanation:

You still have to find the constant of proportionality, it's just going to be a bit faster this way

14/8 = 1.75

21/1.75 = 12

s = 12

A teacher has 396 pieces of candy. If there are 44 students, 6 of whom are boys, if divided evenly, how many pieces of candy will each student get?

Answers

Answer:

9 pieces of candy.

Step-by-step explanation:

The information about how many boys there are is irrelevant, so we can just ignore that.

The important information is that the teacher has 396 pieces of candy and that it is split between 44 students equally.

So, to solve, we just do 396 / 44 = 9.

Therefore, each student will get 9 pieces of candy.

Whats the answer does anyone know

Answers

Answer:

I think it's 12.96

Step-by-step explanation:

Answer:

1.8*1.8=3.24

3.24*4= 12.96

Suppose (−7, 3) is reflected across the x-axis, and then the y-axis.

What will be the new coordinates?

Answers

the answer is (7,-3) ............

Answer:

(7, –3)

Step-by-step explanation:

did it on edgen

The graph of g(x) goes through the point (-4, 1) and is parallel to h(x) = 5x - 2 points
8. Determine the symbolic representation of g(x). Express your answer in
slope intercept form. *

Answers

Answer:

[tex]g(x)=5x+21[/tex]

Step-by-step explanation:

The slope of g(x) is 5 because the slope of h(x) is 5 and g is parallel to h.

In point-slope form:

[tex]g(x)-1=5(x+4)[/tex]

Rearranging for slope intercept form:

[tex]g(x)-1=5x+20\\g(x)=5x+21[/tex]

plz i want the answer

Answers

Answer:

it's answer is E. S = (t² - 2p) / a

Step-by-step explanation:

As

t² = 2p + as

Making s subject then

as = t² - 2p

s =( t² - 2p) / a

Hope it will help :)

I WILL GIVE BRAINLIEST AND POINTS HELP PLEASE

Answers

Answer:

The intersection is at (0,1)

Step-by-step explanation:

What is 1/6 to a percent?

Answers

Answer:

16.666…%

your welcome

Answer:

16.666%

Step-by-step explanation:

If Jimmy has 5 apples and Sandra gives him 2 more how much does he have?​

Answers

Answer:

He has 7

Step-by-step explanation:

5 plus 2 equals 7

Answer:

7 apples

Step-by-step explanation:

5 + 2 = 7

HELP ME FAST! I NEED TO TURN THIS ASSIGNMENT IN SOON!!!!

What are the solutions of the quadratic equation below? [tex]x^{2}-4x-6=0[/tex]


A. [tex]x=2±\sqrt{2}[/tex]

B. [tex]x=2±\sqrt{10}[/tex]

C.[tex]x=-2±\sqrt{2}[/tex]

D.[tex]x=-2±\sqrt{10}[/tex]

Answers

Answer:

b or d

Step-by-step explanation:

AnOtHer geometry question.

Answers

Answer:

the answer is 8!

Step-by-step explanation:

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