The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

A graph with two linear functions; f of x passes through 5, 0 and 10, 10, and g of x passes through negative 3, 0 and 2, 10.

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

Answer 1

Answer:

A linear function can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We know that line f(x) passes through points (5, 0) and (10, 10)

Then the slope of f(x) is:

a = (10 - 0)/(10 - 5) = 10/5 = 2

then:

f(x) = 2*x + b

again, knowing that f(10) = 10   (because this line passes through point (10, 10) )

10 = 2*10 + b

10 = 20 + b

10 - 20 = b = -10

Then the equation of this line is:

f(x) = 2*x - 10

Now for g(x) we know that it passes through (-3, 0) and (2, 10)

then the slope is:

a = (10 - 0)/(2 - (-3)) = 10/5 = 2

g(x) = 2*x + b

And knowing that g(2) = 10   (because this line passes through point (2, 10) )

10 = 2*2 + b

10 = 4 + b

10 - 4 = b

6 = b

then:

g(x) = 2*x + 6

Then the equations are:

f(x) = 2*x  - 10

g(x) = 2*x + 6

A) One transformation may be a vertical translation, and the other can be a horizontal translation.

This is a vertical translation, which is defined as:

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

g(x) = f(x) + k

If k is positive, the translation is upwards

if k is negative, the translation is downwards.

And an horizontal translation of k units is written as:

g(x) = f(x - k)

if k is positive, the translation is to the right

if k is negative, the translation is to the left.

B)

For the vertical translation we have:

g(x) = f(x) + k

2*x + 6 = 2*x  - 10 + k

6 = -10 + k

6 + 10 = k

16 = k

For the horizontal translation we have:

g(x) = f(x - k)

2*x + 6 = 2*(x - k) - 10

2*x + 6 = 2*x - 2*k - 10

6 = -2*k - 10

6 + 10 = -2*k

16 = -2*k

16/-2 = k

-8 = k

C)

The transformations are:

g(x) = f(x) + 16

or

g(x) = f(x - (-8))


Related Questions

WILL GIVE BRAINLIEST

Answers

If I’m correct the answer is A

Answer:

They only intersect once. (Correct letter is B)

Step-by-step explanation:

Slope Intercept Form:

2x - 4y = 3

-2x        -2x

________

-4y = -2x + 3

Switch the signs of all of the numerals since you cannot have a negative 'y' value.

4y = 2x - 3

----   ---------

4         4

y= 1/2x - 3/4

-----------------------------------------------------------------------------------------------------------------

7y - 5x = 8

    +5x  +5x

----------------

7y = 5x + 8

----   ---------

7        7

y= 5/7x + 1 1/7

-----------------------------------------------------------------------------------------------------------------

After graphing the lines, you then can see that the lines only ever intersect once.

Find the perimeter of the given figure, help please!

Answers

Answer:

22.5 cm

Step-by-step explanation:

P=2(6.75)+2(4.5)

P=13.5+9

Please help me find the answer ASAP

Answers

Answer:C Because there the same sides

what is the answer??? Please help me!
16% of 40 =

Answers

Answer:

16/100*40

32/2

lol so simple

gg

The area of a rectangle is 192 in ^2. The ratio of the length to the width is 4:3. Find the length and the width.

The length of the rectangle is ___ in.
The width of the rectangle is___.

Answers

Answer:

Length = 16 in

Width = 12 in

Step-by-step explanation:

Given:

Area of a rectangle = 192 in²

Ratio(length to width) = 4:3

Find:

Length and the width

Computation:

Ratio(length to width) = 4:3

So,

Length = 4a

Width = 3a

Area of a rectangle = Length x Width

192 = 4a x 3a

192 = 12a²

a² = 16

a = 4

Length = 4a = 4 x 4 = 16 in

Width = 3a = 3 x 4 = 12 in

short song i made what yall think of it?

Answers

this is good keep it up stan u sound cloud rappa 4 life

Please help me with those questions please

Answers

Answer:

7.5

35.2

1.5

20

Step-by-step explanation:

1. vertical angles are equal

(2x+17)=(4x+2)

15= 2x

x= 7.5

2. adjacent angles equal 180

(2m+8)+(3m-4)= 180

5m+4= 180

5m= 176

m= 35.2

3. (30s+5)=(20s+20)

10s= 15

s=1.5

4. 4p+5p=180

9p=180

p=20

sorry that took so long.  I was babysitting lol

LOOK I really new help on this I will give u cash for it just give me your cash app or Venmo please help this is so many points
question
(60-5.8) ÷ 5 - 3^2
can you please explain it in an essay type like words and not just show me the answer I need it to show me how you got the answer don't give me just the answer

Answers

Answer:

1.84

Step-by-step explanation:

First you solve what is in the parenthesis.

60 - 5.8 = 54.2

The equation is now 54.2 ÷ 5 - 3^2

Now, you do the exponents. 3^2 = 9 since 3 to the second power is just another way to write 3 x 3.

Your equation is now 54.2 ÷ 5 - 9

You then divide 54.2 ÷ 5

54.2 ÷ 5 = 10.84

The last equation is 10.84 - 9

10.84 - 9 = 1.84

Answer:

Answer 1.84.

Step-by-step explanation:

The first person's answer and explanation is correct.

60 centimeters every 2.5 years 30 centimeters every 15 months are these equivalent? I NEED IT MY TEST IS TOMORROW and I am just really stumped on this.

Answers

Answer:

Yes, they are equivalent

Step-by-step explanation:

15 months= 1.25 years

60/2.5= 24

30/1.25 = 24

Answer:

Step-by-step explanation:

Since 2.5 years equals 2.5(12)=30months you have

60cm/30mo and 30cm/15mo these are equivalent because (2/2)(30/15)=60/30

20=c/5

can you show your work thanks
Someone help me I need this one fast

Answers

c = 20 × 5

c = 100

and that's all

Answer:

Step-by-step explanation:

WILL GIVE BRAINLIEST

Answers

6²+ 8²= 10²

36 + 64 = 100

100 = 100

so yes because 6² + 8² = 10²

Option B

Hand Sanitizer question​

Answers

Answer:

the first one  

Step-by-step explanation:

Can someone plz help me with this the answer choices are at the bottom plz I beg u

Answers

formula is v=1/3Bh
shape of base is rectangle/parallelogram
solution: 192cm^3
sorry if it’s wrong , been a while since i did it

Answer:

Step-by-step explanation:

A new car is for lease for $429 per month with a down payment of $1,058. What is the cost for 42 months for this vehicle?

$19,076

$44,865

$44,436

$18,018

$62,454

Answers

18,018 is the answer

NEEED HELP PLEASEEEEE
Write a rate that represents the situation:
One possible rate is ( ) week(s) for ( ) every day(s).

Answers

Answer:

10/10

Step-by-step explanation:

Ez..........................................................

how to slove
y=15x+12

Answers

Answer:

0

Step-by-step explanation:

If CD is not parallel to EF, what is m2C?

Answers

Don’t open they takes all your information it’s a scam

write an equation for the following problem

Answers

Answer:

x+68=90 degrees

Step-by-step explanation:

Answer:

90-68 or 68+22

Step-by-step explanation:

this works becuz it is a 98 degree angle

sketch graphs of these three quadratic relations on the same set of axes.
a) y=x^2 + 8
b) y= x^2 - 5
c) y= x^2 - 10

Answers

Answer: B
I hope this helps you

5.solve for x 6. solve for x​

Answers

Answer:

x=10 , x=13

Steps:

5.

4x+5x=180-90

9x=90

x=90/9

x=10

6.

(3x+7)+(2x+3)=180-105

5x+10=75

5x=65

x=65/5

x=13

Step-by-step explanation:

☯ [tex] \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T\: I \: O \: N}}}} : [/tex]

✰ [tex] \underline{ \underline{ \large{ \text{For \: Question \: Number \: 5}}}} : [/tex]

[tex] \large{ \tt{90 \degree + 4x \degree + 5x \degree = 180 \degree}}[/tex] [ Sum of angle in a triangle ]

⤑ [tex] \large{ \tt{90 \degree + 9x \degree = 180 \degree}}[/tex]

⤑ [tex] \large{ \tt{9x \degree = 180 \degree - 90 \degree}}[/tex]

⤑ [tex] \large{ \tt{9x \degree = 90 \degree}}[/tex]

⤑ [tex] \large{ \tt{ \frac{9x}{9} = \frac{90}{9} \degree}}[/tex]

⤑ [tex] \boxed{ \large{ \tt{x = 10 \degree}}}[/tex]

----------------------------------------------------------

✰ [tex] \underline{ \underline{ \text{For \: Question \: Number \: 6}}} : [/tex]

[tex] \large{ \tt{75 \degree = 3x \degree + 7 \degree + 2x \degree + 3 \degree}}[/tex] [ Exterior angle is equal to the sum of two non-adjacent interior angles ]

⟶ [tex] \large{ \tt{75 \degree = 5x \degree + 10 \degree}}[/tex]

⟶ [tex] \large{ \tt{5x \degree \: + 10 \degree = 75 \degree}}[/tex]

⟶ [tex] \large{ \tt{5x \degree = 75 \degree - 10 \degree}}[/tex]

⟶ [tex] \large{ \tt{5x \degree = 65 \degree}}[/tex]

⟶ [tex] \large{ \tt{ \frac{5x}{5} = \frac{65}{5} \degree}}[/tex]

⟶ [tex] \boxed{\large{ \tt{x = 13 \degree}}}[/tex]

Hope I helped ! ✧

Have a wonderful day / night ! ♪

Let me know if you have any questions regarding my answer!

[tex] \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}[/tex] !! ♕

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁


Sally flipped a penny 25 times and landed on heads 16 out of the 25 times. If she plans to flip the coin 100 times,
how many times can she expect to land on heads?

Answers

Answer:

50 times

Step-by-step explanation:

Since the odds of her getting a heads is 50% (1/2) every time she flips the coin. So she should expect to get 50 heads. However this number varies practically because in every single flip there is a 50-50 chance. If she had flipped it infinitely many times then it would be exactly 50%

What is the equation of a line with a slope of 2 and a y intercept of -5?

Answers

Answer:

y=2x-5

Step-by-step explanation:

The slope is how you move so you could also call it m

The y intercept is where you begin so you could call it b

So every time you need to find the equation or which one is like the slope just remember m=move b= begin

y=mx+b

Help!! I have 55 seconds to do this

Answers

Answer:

the answer is A

Step-by-step explanation:

78 is acute angle because it is less than 90 degrees. A is an acute angle so thats the answer

Rectangle A'B'C'D' is the image of rectangle ABCD after a dilation. What is the scale factor of the dilation?​

Answers

The dilation is 1/2
The second image is 1/2 the length of the original image

Is this correct and if not what am I missing?

Answers

it would be B. because the others aren’t correct

Answer:

Yes you are correct

The peak is at 5

Step-by-step explanation:

PLS HURRY AND HELP
Darren had 3 apples represented by the variable (a) . He went to the store and bought 6 more apples to make a pie . Then his little brother Keith came into the kitchen and ate 2 of the apples. Write an expression to show how many Derran is left with.

Answers

Answer:

a + (6 -2)

I'm not completely sure, but I hope this helps.

Im new to this tysm though if you help!:)

Answers

Answer:

60

Step-by-step explanation:

-12 * -5 = 60

Answer:

60

Step-by-step explanation:

Hey!

When you multiply a negative by a negative you get a positive, because the two negative signs are cancelled out.

So -12(-5) is equivalent to 12(5) which is 60.

Hope I helped, Feel free to ask any questions if you need me to clarify!

Have a nice day!

            -Aadi x

The measure of angle 1 is 39º. What is the measure of the angle
adjacent to angle 1? Explain.

Answers

Answer:

[tex]180 - 39 = 141[/tex]

141° is the answer

Mason is laying tiles on his entryway. The tiles are each 2/9 feet long, and the entryway is 7 1/2 feet long. How many tiles will Mason need to buy in order to cover the length of the entryway? Explain.

Answers

Answer:

1 2/3

Step-by-step explanation:

7 1/2x2/9

The required number of tiles will be 34 covering the length of the entryway.

What is the Multiplication operation?

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

We have been given that the tiles are each 2/9 feet long, and the entryway is 7 1/2 feet long.

We have to determine the number of tiles will he need to buy in order to cover the length of the entryway.

According to the given question, the required solution would be as:

So the number of tiles covering the length of the entryway will be

⇒ 7 1/2 ÷ (2/9)

⇒ 15/2 ÷ (2/9)

⇒ 15/2 / (2/9)

Reciprocal the term in the denominator

⇒ (15/2) x (9/2)

Apply the multiplication operation,

⇒ 135/4

Apply the division operation,

⇒ 34

Thus, the required number of tiles will be 34 covering the length of the entryway.

Learn more about Multiplication operations here:

brainly.com/question/25834626

#SPJ5

2. Given that set M = {Even numbers between 20 and 35), find n(m)​

Answers

Step-by-step explanation:

Set M = {20,22,24,26,28,30,32,34}

n(M) = no. of elements in set M

i.e.

n(M) = 8

Answer:

7

Step-by-step explanation:

Even numbers between 20 and 35 are 22, 24, 26, 28, 30, 32, 34.

M = { 22, 24, 26, 28, 30, 32, 34}

There are 7 elements in the set M.

Thus, n(M) = 7

Other Questions
Identify two functions of international law in conflict situations. Review Paragraph 5. What factor would not affect the island lizard gene pool once theyreached the mainland? How many equal sections divide a directed line segment if it is to be partitioned with a 2:7 ratio? 2, the least number given in the ratio2, the least number given in the ratio14, the least common multiple of the numbers given in the ratio9, the sum of the numbers given in the ratio5, the difference of the numbers given in the ratio7, the greatest number given in the ratio Which of the following economic shifts resulted most directly from the trends described in the excerpt? Choose 1 A The emergence of the Silk Road, a trade route between Europe and Asia B European economies shifted from a feudal economy to a capitalist economy Native American economies shifted from capitalist economies to feudal economies A religious caste system in the New World Please help, this is due soon! If I have 14 neutrons and 11 electrons, what is my mass number?A.25B.3C.11D.14 Decide whether the sentence is grammatically CORRECT or INCORRECT as written. A Juan le gusta ir de vacaciones. Is this equation balanced: AgNO3 + 2 KCl -->AgCl + KNO3 Yes No If Enough Thermal energy And change of state, write each sentence.Write (solid), (liquid), or (gas) to complete each sentenceIf enough Thermal energy is added to a liquid, it will change to a___________Please explain in simple terms.Spam = removeGoogling it = Remove Which of the following is a statistical question? A. How many girls named Jennifer are there in the class? B. What is the age of students in Ron's school? C. How many artifacts are there in the museum? D. What is the capital of Texas? Insert two dashes where needed. - New DNA evidence suggests that the kiwi a small, flightless bird found in New Zealand is closely related to the enormous, extinct elephant bird. What decimal is equivalent to 8/40? SIMPLE 7TH GRADE MATH PROBLEM?!?! If these four countries trade only with each other, what is the difference between the highest balance of trade and the lowestbalance of trade within this group?a 4,378,000,0002,797,000,0001,928,000,000d 738,000,000 factor g(x) =6x^3 +13x^2 -2x -1 if (2x + 3) is a factor. Help... need it right now ;-; Discuss the ways in which international 5 star hotels meet theneeds of family visitors, travelling with young children. help! parallel, perpendicular, or neither? Why is there no answer Which of the following is NOT a way hitler defied the Treaty of Versailles.A. Created an alliance with Italy and Japan.B. Moves troops into Rhineland C.Expands the German military D. Stops paying reparations