Determine the transformations that produce the graph of the functions g(x)=0.2log(x+14)+10 and h(x)=5log(x+14)−10 from the parent function f(x)=logx. Then compare the similarities and differences between the two functions, including the domain and range.

Answers

Answer 1

Let's focus on g(x) for now.

0.2 = 1/5

f(x) = log(x) is the parent function

0.2*f(x) = 0.2*log(x) .... vertical compression by factor of 5

0.2*f(x+14) = 0.2*log(x+14) .... shift 14 units to the left

0.2*f(x+14)+10 = 0.2*log(x+14)+10 .... shift 10 units up

g(x) = 0.2*log(x+14)+10

The transformations to go from f(x) to g(x) are:

vertical compression by factor of 5shift 14 units to the leftshift 10 units up

The domain of g(x) is x > -14 to ensure that x+14 > 0. This is so we avoid applying a log to 0 or a negative value. The parent function domain was x > 0. Note how the domain shifted 14 units to the left (step 2)

======================================================

Now onto h(x)

f(x) = log(x)

5f(x) = 5log(x) .... vertical stretch by factor of 5

5f(x+14) = 5log(x+14) ... shift 14 units left, just like earlier

5f(x+14)-10 = 5log(x+14)-10 ... shift 10 units down

h(x) = 5log(x+14)-10

The transformations to go from f(x) to h(x) are:

vertical stretch by factor of 5shift 14 units to the left (same as g(x))shift 10 units down (instead of up compared to g(x))

This time h(x) is taller compared to f(x), while g(x) is more vertically squished compared to f(x). Both involve being shifted 14 units to the left, so both g(x) and h(x) have the same domain. Vertical shifting and compressing/stretching does not affect the domain.

The range of f(x), g(x) and h(x) is the set of all real numbers.


Related Questions

What is the equation of the line that passes through the point (3, -5) and has a
slope of 2/3?

Answers

The answer is this I have to have 20 words in here but here is the answer Y=2/3x-3

Which one?
A. B. C. or ​

Answers

Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Which calculation will always give a result greater than 1?
5 x a number less than 1
1 3/4 - a fraction less than 3/4
4/9 + a fraction less than 1/2
7/8 x a number less than 1

Answers

Answer:

1 3/4 - a<3/4

proof:

1 3/4 -a<3/4

=>1 3/4 - 1 3/4 -a<3/4- 1 3/4

=>-a<-1

=>a>1

Find the unit rate of miles per gallon for these vehicles

Sedan:
Minivan:
Truck:

Answers

Answer:

Sedan: 18

Minivan:19

Truck: 16

Step-by-step explanation:

Got it right on edge

If you don't trust me sorry but i got it right

Jada is training for a marathon. She wants to run a total of 25 miles this week. She will run the same distance each day for 6 days. How many miles will she run each day?

Answers

Answer:

4 1/6

Step-by-step explanation:

4 x 6 = 24

1/6 x 6 = 6/6 = 1

24 + 1 = 25 :)

8800000 in scientific notation

Answers

Answer:

8.8 x 10 to the power of 6

Step-by-step explanation:

i need help on this

Answers

Answer:

2

Step-by-step explanation:

63/9 = 7 and -5 + 7 is the same thing as 7-5 so it's 2

Answer:

2

Step-by-step explanation:

[tex]\frac{63}{9} = 7[/tex]  Plug 7 in: -5 + 7-5 + 7 = 2

I hope this helps!

how do you do 4+1346=? 600x787 and 675dividedby700=

Answers

Answer:

How do you do 4+1346=? AnswerL 1350

600x787 and 675dividedby700= 472200  :D

Step-by-step explanation:

Answer:

4+1346=1350 ... 600x787=472200

675÷700=0.96

What is the value of the 4 in the number 546210?
Give your answer in words

Answers

Answer:

Ten Thousands

Thank you ☺️☺️

50 points plus Brainnlest for right answer

What is the equation?
What should you replace for each given variable?
What should you solve for?

Answers

Equations: 60x + 3000 = 3,000, 600 + 150y = 3000

X: 20

Y: 10

You should solve for x & y

Q1: 0, it's already filled up to the max of 3000 pounds.

Q2: 16, 60 times 10 is 600. 3000-600 = 2400. 2400/150 = 16

I hope this helped, ask if you need more help :)

I don't understand this at all. Can you help me solve this please :) ​

Answers

Answer:

y = -1/2x +3

Step-by-step explanation:

basically all you have to do is change the y intercept, but keep the slope the same and you create a parallel line

What is the equation of the line passing through the points (2, -1) and (5, -10) in slope intercept form

Answers

Answer:

-3x+5

Step-by-step explanation:

y2-y1/x2-x1

if the centroid of the triangle formed by (x,0), (5.2) and (-8.y) is at (-2,1) then (x,y) is equal to
only proper people will be given this mark...or else will fire u from brainly...​

Answers

Answer: Hola, ila munkililakum ghithishalan fee mabruk ilal habeebi

PLEASE HELP ME OUT

John has two coupons to use at a clothing store. One is for $20 off and
the other is for 20% off. John wants to purchase a shirt with one of the
coupons and wants to pay the least amount that he can. Choose the
answer that BEST describes the situation.
A. The shirt will have the lowest price with the $20 off coupon
B. The shirt will have the lowest price with the 20% off coupon.
C. The shirt will cost the same with either coupon.
D. It depends on the cost of the shirt as to which coupon will help John pay the lowest
price

Answers

Answer: D. It depends on the cost of the shirt as to which coupon will help John pay the lowest price.

Step-by-step explanation:

You do not know how much a 20% discount is unless you know the price of the shirt. This can be more or less than $20, so you don’t know.

Hope this helps!

Answer:

D.

Step-by-step explanation:

For example if a shirt was $100 dollars, 100-20 = 80 and 100 x .8 = 80

But if the shirt cost $35, 35-20 = 15 while 35 times .8 = 28

This shows that the cost of the shirt is important in discovering which coupon is better.

What is the square root of 51.84​

Answers

The square root of 51.84 is 7.2

Y is 5 less than the product of 4 and x

Answers

Answer: y=4x-5

Y=4x-5

A number is written with 10 zeros, 10 ones and 10 twos. Is it possible for it to be a perfect square ? Please help. I don’t understand how to solve this...

Answers

Answer:

i am going to help you to understand this problem. if it is written with 10 0s it will be the billion place. because of the ten ones it will be 0,000,010, and because of the ten two's, which is 20, it will be 0,000,030. and when i searched up on google, and watched an episode of number blocks, no, 30 is not a square number OR a cube number.

Step-by-step explanation:

A stack of 3 books weighs 7.8 kilogramh book weighs the s. If eacsame amount, how much does each book weigh?

Answers

Answer:

they each way 2.6 kilograms

HELP ASAP: Can you draw a quadrilateral that's not a parallelogram with only one pair of congruent angles? Explain why one pair of congruent angles isn't enough information to prove that a quadrilateral is a parallelogram.

Answers

Yes it is possible. We could draw a trapezoid that has 2 right angles as shown below. A trapezoid has only one pair of parallel sides. A parallelogram needs both pairs of opposite sides to be parallel.

Yes, it is conceivable. As shown below, we could draw a trapezoid with two right angles.

What is quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners in geometry. A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are known as the trapezoid's bases.

Yes, it is conceivable. As shown below, we could draw a trapezoid with two right angles. A trapezoid has only one parallel pair of sides. Both pairs of opposite sides of a parallelogram must be parallel.

The shape of the required quadrilateral is attached with the answer below.

To know more about quadrilaterals follow

https://brainly.com/question/16691874

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What is the solution to 4x3 - 3x2 - 7x<0?

Answers

Answer:

[tex](-∞,1) , (0,\frac{7}{4})[/tex]

Step-by-step explanation:

Factor:

x(4x³-3x-7)<0

The point (1, –5) is reflected across the y-axis. A coordinate plane. What are its new coordinates?

Answers

Answer:

(-1,-5)

Step-by-step explanation:

Answer:

HMM C..... Answer:  Choice C.   (-1, -5)

Step-by-step explanation:

The reflection rule we use is

when we want to reflect over the y axis. The x coordinate flips from positive to negative, or vice versa, while the y coordinate stays the same.

If you have the equation of different situations into y = mx + b, What do m and b represent?
A
m represents the y-intercept and b represents the slope.
B
m represents the growth and b represents the initial value.
m represents the slope and b represents the y-intercept.
D
m represents the growth and b represents the Figure #0.

Answers

Answer:

C. m represents the slope and b represents the y-intercept.

Step-by-step explanation:

The equation of straight line is usually expressed as:

       y  = mx + b

Where y is the vertical axis component

           x is the horizontal axis component

           m is the slope

           b is the y-intercept

At the y-intercept, x = 0

Also, the slope is the rise divided by the run.  

please help thank you!!!

Answers

Answer:

s = 11.7 ft

Step-by-step explanation:

The bedroom is square, and the area A is equal to 137 ft^2.

Since the area formula for a  square is A = s^2, s = √A.

Here, s = √137 ft, or s = 11.7 ft (to the nearest tenth of a ft)

Which pair of functions are inverses of each other?

Answers

Answer:

A

Step-by-step explanation:

Inverse means that the function is reversed from the original function, f(x).

To find the inverse function of f(x)=5x-11, add 11 to x, then divide the expression by 5.

This would be (x+11)/5.

So, you know that A is true.

Try the other selections too.

B: [tex]g(x)=x^3/2[/tex]       The x should be tripled before being divided by 2; FALSE

C: [tex]g(x)=7/(x+9)[/tex]     7 should by in the numerator; FALSE

D: [tex]g(x)=6(x+8)[/tex]    8 should be added before being multiplied by 6; FALSE

I hope this helps!!!

Using composite functions, it is found that the pair of functions that are inverse of each other is given by:

A. [tex]f(x) = 5x - 11[/tex] and [tex]g(x) = \frac{x + 11}{5}[/tex]

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

The composite of functions f and g is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

Two functions f and g are inverse of each other if:

[tex]f(g(x)) = g(f(x)) = x[/tex]

Item a:

[tex]f(x) = 5x - 11[/tex]

[tex]g(x) = \frac{x + 11}{5}[/tex]

[tex]f(g(x)) = f(\frac{x + 11}{5}) = 5(\frac{x + 11}{5}) - 11 = x + 11 - 11 = x[/tex]

[tex]g(f(x)) = g(5x - 11) = \frac{5x - 11 + 11}{5} = \frac{5x}{5} = x[/tex]

Since [tex]f(g(x)) = g(f(x)) = x[/tex], these functions are inverse of each other.

A similar problem is given at https://brainly.com/question/23458455

find the missing angle in the image below?

Answers

Answer:

? = 40°

Step-by-step explanation:

100° = 60° + ? (The exterior angle property of triangles)

100° - 60° = ? (By the law of transposition)

40° = ?

If my answer helped, kindly mark me as the brainliest!

Thank You!

Answer:

the missing angle is 40

Step-by-step explanation:

let the missing angle be x

then x+ 60 = 100 using (exterior angle property)

so x= 100-60 which is equal to 40.  

hope this helps u buddy..

How many four-digit numbers can you make with these three integers?
0, 1, 2

Answers

Answer:

I would think 2222

Step-by-step explanation:

Between the three numbers, that four-digit number is the greatest.

(Apologies if not correct)

Which mathematical concepts did Euler's legacy include? Check all that apply.

the notation for the imaginary unit
the idea of a functional relationship
the formalization of function notation
the definition of a circle's circumference
the notation for the base of the natural logarithm

Answers

Answer:

a)the notation for the imaginary unit

c) the formalization of a function notation

e) the notation for the base of the natural logarithm

Step-by-step explanation:

it said i was correct :P

the notation

the formalization of function notation

the notation for the base of natural logarithm

Help ASAP!!!!! Due in 5 minutesp

Answers

Answer:

-1/2

Step-by-step explanation:

to find perpendicular slope, flip the number and the sign

Caleb starting playing video games as soon as he got home from school. He played video games for 50 minutes. Then Caleb helped clean the kitchen for 1 hour. After the kitchen was clean, it took Caleb 1 hour and 55 minutes to finish his homework. When Caleb finished his homework, it was 7:40 P.M. What time did Caleb get home from school?

Answers

Answer:

Caleb had gotten home at 3:55 pm

Answer:

Caleb got home around 3:55

Step-by-step explanation:

Find the value of 5x+6 when x=-2

Answers

Answer:

-4

Step-by-step explanation:

5 times negative -2 is -10 and you just add 6 so the answer is -4

The value of 5x + 6 when x = -2 will be -4.

What is Expression?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is the following expression -

5x + 6

Given is the following expression -

5x + 6

At x = -2, we can evaluate the expression as -

5x + 6

5 x -2 + 6

-10 + 6

-4

Therefore, the value of 5x + 6 when x = -2 will be -4.

To solve more questions on Evaluating expression, visit the link below-

https://brainly.com/question/13589173

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