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

The radius of a sphere with a volume of 4.5 cubic mm is ___ mm.

Answers

Answer:

2.5 mm

Step-by-step explanation:

A paved walkway around a garden has an outer diameter of 80 ft and an inner diameter of 40 ft. A diagram is shown below.
What is the approximate area of the paved walkway?

Answers

Given:

Outer diameter = D = 80 ftInner diameter = d = 40 ft

So,

Outer radius = R = D/2

=> R = (80 ft)/2

=> R = 40 ft

Inner radius = r = d/2

=> r = (40 ft)/2

=> r = 20 ft

Area of paved pathway = πR² - πr²

= π(R² - r²)

= π(R + r)(R - r)

= π(40 + 20)(40 - 20) ft²

= π(60)(20) ft²

= 3.14 * 1200 ft²

= 3768 ft²

Skully played basketball on a team. He has played four games so far. In the first
game, he scored 24 points. In the second game, he scored 14 points. In the third
game, he scored 17 points and in the fourth game he scored 22 points. What is Skully
average points per game>

Answers

Answer:

19.25

Step-by-step explanation:

24 + 14 + 17 + 22 = 77

77 ÷ 4 (The number of matches) = 19.25

2 ft 12 ft

what is the surface area and volume​

Answers

5.12? Maybe 24? I’m sorry if there wrong which they probably are. Sorry :(

help me pleaseeeeeeeeeeeeeeeeeeeeeeeee!!!!

Answers

Answer:

39 is sydney age

39 +39 is 78 and they said two times


A cube has a total surface area of 150 inches squared. Considering every side length is
congruent, and every face equivalent on a cube, what is the side length?

Answers

Answer:25.0

Step-by-step explanation: 5.0 times 5.0

i still haven't finished this and it's due today. i really would appreciate some help .

Answers

A
x X x
= x^2

B
20 x 20 = 40

C
100 / 40 = 2.5 per square inch


Find the equation of the line which passes through (4, -1) and (2, -1).

Answers

Answer:

y = -1

Step-by-step explanation:

As part of a survey, 500 boys were asked to name their favorite car. The results showed that 30 of the boys named a Corvette as their favorite car. What percentage of the boys in the survey named a Corvette as their favorite car?
A-6%
B-0.6%
C-60%
D-40%

Answers

A-6%
30 ÷ 500 = 0.06 = 6%

You earned (and saved) $3500 last summer weed whacking. Your folks tell you to get a savings account. You put all the money in one that pays 3% interest. How much would be in the account in 20 years?

Answers

Answer:

2100

Step-by-step explanation:

Answer:

2100

Step-by-step explanation:

answer this please i need this​

Answers

Answer:

x=121°

Step-by-step explanation:

the sum of angles in a triangle always equal 180°

that means that 22°+37°+x°=180°

so we solve the equation by isolating the variable

add 22 and 37 together

59°+x°=180°

subtract 59 from both sides

x=121°

that means that x is 121 degrees

hope this helps!

Find the missing side round your answer to the nearest tenth

Answers

Answer:

x ≈ 14.7

Step-by-step explanation:

Assuming the triangle is right then use Pythagoras' identity.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 15² = 21²

x² + 225 = 441 ( subtract 225 from both sides )

x² = 216 ( take the square root of both sides )

x = [tex]\sqrt{216}[/tex] ≈ 14.7 ( to the nearest tenth )

I NEED HELPP!!! WHOEVER GETS IT RIGHT GETS BRAINLIEST!!
There needs to be an explanation!!!
So if you don't have one don't answer!

Answers

Answer:

i think its b

Step-by-step explanation

because there are 6 slices and there is 1 red soo

i think its b

sorry if its wrong

but i think its b

Which expression is the equivalent to 23 1/2?

Answers

Answer:

Step-by-step explanation:

Recall that the quantity 25^(1/2) with fractional exponent 1/2 can be rewritten in the equivalent √25.  In other words, the exponential form

25^(1/2) has the same value (outcome) as does √25.

In general, b^(1/a) is equivalent to (index a root of b).

[tex]\sqrt{23}[/tex] is the equivalent expression of [tex]23^{\frac{1}{2} }[/tex]

What is Expression?

An expression is combination of variables, numbers and operators.

Equivalent expression is the expression whose value will be same when we simplify.

The given expression is Twenty three power one by two.

[tex]23^{\frac{1}{2} }[/tex]

By the exponential property.

Root of twenty three is expression equivalent to twenty three power of one by two.

[tex]\sqrt{23}[/tex]

Hence, [tex]\sqrt{23}[/tex] is the equivalent expression of [tex]23^{\frac{1}{2} }[/tex]

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

Y=6-x In this case, what would be the slope and y-intercept? I'm having a hard time trying to get it to the y=mx+b format.

Answers

Answer:

Slope = [tex]\frac{-1}{1}[/tex] or -1

y = 6

Step-by-step explanation:

The equation given (y = 6 - x) is the same as saying

y = -1x + 6

Since we have a negative x variable and a positive 6 and would also be graphed the same. The only difference is that the second equation I just mentioned resembles the y = mx + b expression more. In this case the slope would be

Slope = [tex]\frac{-1}{1}[/tex] or -1

While the y-intercept would be

y = 6 - x

y = 6 - 0

y = 6

Analyze: 30 + 11 when c=4

Answers

It would be 23 because 3(4) + 11 would convert to 12 + 11 giving you 23

Answer:

23

Step-by-step explanation:

3c + 11

3(4) + 11

12 + 11

23

Find the volume of a cylinder in cubic feet

Answers

Answer:

4398.23

Step-by-step explanation:

will give brainliest What are the coordinates of Point A?
A) (1, 2)
B) (-1, 2)
C) (2, 1)
D) (1, -2)

Answers

Answer:

A= (1,2)

Step-by-step explanation:

I hope this helps

have a nice day/night

mark brainliest please :)

Answer:

A) (1, 2)

Explanation:

The origin is (0, 0), where the y-axis and the x-axis intercept (the two lines). You find the coordinates by measuring the point's distance on the both lines from the origin. On the x-axis, (horizontal, the one that goes from left to right) the point is 1 unit to the right, so the x is 1. On the y-axis (vertical, the one that goes from up to down), the point is 2 units to the right, so y is 2. The combined coordinate is (1, 2).

ok i give you free point answer this good luck ​

Answers

Answer:

120

Step-by-step explanation:

Answer: 120

12 x 10 = 120

1/5x1/3 as a fraction please

Answers

Answer:

Step-by-step explanation:

If the (X) in this means times then

1/15

The value of solution of expression is,

⇒ 1 / 15

We have to given that;

Expression is,

⇒ 1/5 × 1/3

Now, We can multiply the numbers as;

⇒ 1/5 x 1/3

⇒ 1 / (5×3)

⇒ 1 / 15

Thus, The value of solution of expression is,

⇒ 1 / 15

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ6

The mall is 6 miles west of the highway. The hospital is 12 miles west of the mall. How far, and in what direction, is the hospital from the highway?

Answers

Answer: 18 miles west

Step-by-step explanation:

The mall is west of the highway.

The hospital is then west of the mall.

If the hospital is west of the mall which is already to the west of the highway, the Hospital must be west of the highway as well.

The hospital is 12 miles west of the mall which is then 6 miles west of the highway. As they are both west, it is a continuous distance and we can simply add their distances up and assume the distance is linear.

The distance between the hospital and the highway is therefore:

= 12 + 6

= 18 miles west

does order matter in division of fractions? for example, is 2 3rds divided by 1 5th the same as 1 5th divided by 3 2s

Answers

Answer:

Order matters in divisions of fractions. If you do not put them in the correct order, you will get different answers

Step-by-step explanation:

What is the quotient?
x + 1)3x2 – 2x + 7
O 3x - 5+
2
X + 1
O 3x - 5+
12
X + 1
2
O 3x + 5 +
2
X + 1
O 3x + 5+
12
X + 1

Answers

Answer:

The answer is the second one .

hey could yall help me this is due at 12 :>

Answers

Answer:

I would say D and B im not 100% sure its just me cause i did the math and

Step-by-step explanation:

A= 13/24

B=7/12

C=4/15

D=1/8

Use the distributive property to write an expression that is equivalent to the expression below. -2 (-6x + 3y - 1)

Answers

Answer:

1 2 − 6 + 2

Step-by-step explanation:

PLS HELP. If the spinner shown below was used 100 times, how many times can you expect to spin a number greater than 3?

3
60
2
40​

Answers

Answer:

60 times

Step-by-step explanation:

Question 9 of 10
Which of the following equations is an example of inverse variation between
the variables x and y?

Y=x/3
Y=3x

Answers

Answer:

1st one........,..............


If the hypotenuse of a right triangle is 8 and one leg is 6, what is the length of the other leg?

Answers

Answer:

5.3

Step-by-step explanation:

pythagorean theory :,)

[tex]a^{2} + b^{2} = c^{2}[/tex]

the legs are [tex]a[/tex] and [tex]b[/tex], while the hypotenuse (the longest side) is [tex]c[/tex]

fill in the equation with the information u have and simplify so

[tex]a^{2} + 6^{2} = 8^{2}[/tex]

[tex]a^{2} + 36 = 64[/tex]

now get the variable ([tex]a[/tex]) by itself

[tex]a^{2} + 36 = 64\\[/tex]

(subtract 36 on both sides)

[tex]a^{2} = 28[/tex]

[tex]a = 5.3[/tex]

square root of both sides ≈ 5.3

(you could also multiply the square root of 7 by 2)

Omg guys I need help with this question I've failed the test like 4 time because of this question and I give up. Can someone please help me with this?

Answers

Answer:

D. 270

Step-by-step explanation:

With the information given you can work your way around the table to fill in the blanks

300-120=180 Red-footed one-headed

180+200=380 total red-footed

650-380=270 total black-footed (answer)

270-120=150 black-footed two-headed

150+200=350 two-headed

Answer:

270

Step-by-step explanation:

300-120=180,to get one headed red footed

650-300=350, total two headed.

350-200=150, to get two headed black footed.

150+120=270, total black footed mizjigs

TTriangle H L I is shown. Line segment J K is drawn near point L to create triangle J L K. If △HLI ~ △JLK by the SSS similarity theorem, then StartFraction H L Over J L EndFraction = StartFraction I L Over K L EndFraction is also equal to which ratio? StartFraction H I Over J K EndFraction StartFraction H J Over J L EndFraction StartFraction I K Over K L EndFraction StartFraction J K Over H I EndFraction

Answers

Question:

[tex]\triangle[/tex]HLI is shown. Line segment JK is drawn near point L to create [tex]\triangle[/tex]JLK. If [tex]\triangle[/tex]HLI ~ [tex]\triangle[/tex]JLK by the SSS similarity theorem, then [tex]\frac{HL}{JL} =\frac{IL}{KL}[/tex] is also equal to which ratio?

[tex]\frac{H I}{J K}[/tex]      [tex]\frac{H J}{J L}[/tex]     [tex]\frac{I K}{K L}[/tex]     [tex]\frac{J K}{H I}[/tex]      

Answer:

[tex]\frac{H I}{J K}[/tex]

Step-by-step explanation:

Given

HLI ~ [tex]\triangle[/tex]JLK

[tex]\frac{HL}{JL} =\frac{IL}{KL}[/tex]

Required

Which other ratio equals [tex]\frac{HL}{JL} =\frac{IL}{KL}[/tex]

[tex]\triangle[/tex]HLI ~ [tex]\triangle[/tex]JLK  implies that:

HL, IL and HI corresponds to JL, KL and JK respectively.

So, the possible ratios are:

HL : IL : HI = JL : KL : JK

Convert to fractions

[tex]\frac{HL}{JL} = \frac{IL}{KL} = \frac{HI}{JK}[/tex]

So, from the list of options

[tex]\frac{H I}{J K}[/tex] is equivalent to [tex]\frac{HL}{JL} =\frac{IL}{KL}[/tex]

Answer:

its A

Step-by-step explanation:

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